I wanna be smart about this, and not just listen to them say they can give me this or that rate or payment. I gotta figure out what’s the best deal, see?

I don’t got nothin’ for a down payment, you know how it is. Not like I was expecting to fall for this sweet baby. So that’s $28,000 bucks I’m dealin’ with, on the round. Here’s my choices:

$3,000 bucks off and 4.9% interest for 60 months

Full price and 1.9% interest for 48 months

Which one is the best deal? That’s what I want to know… then I’ll see if I can afford the payments. I’m gonna make this easy and figure the total cost of the interest is (Price) x (Interest) x (Years). That’ll give me a good approximation of what I’m paying. So I can fly fast and figure this out.

So which one’s the best deal? Can you figure it out? I’ll let you know what I figured next week.

1. $3,000 bucks off and 4.9% interest for 60 months
2. Full price and 1.9% interest for 48 months

Here’s the formula:

(Price) x (Interest) x (Years) = total interest

So here’s how to figure the interest for the two deals… see how to get number of years, I divide months by 12? 12 months in a year…

1. ($27,599 – $3,000) x 4.9% x (60/12)
2. $27,599 x 1.9% x (48/12)

Now, it’s just doin’ the math, right… let’s start with the first one… 27 minus 3, is 24. And 60 months are 5 years. Don’t hardly need to know the math.

1. $24,599 x 4.9% x 5

On the second on, all you gotta do is divide 48 by 12… four years.

1. $24,599 x 4.9% x 5
2. $27,599 x 1.9% x 4

You can break out a calculator now to figure this one out….

1. $6,026.755
2. $2,097.524

Damn, the second one’s got like $4,000 less interest. The first one, though, the price is $3,000 cheaper. So if I go with the second deal, I’m payin’ $1,000 less. On the downside, the payments are higher… gotta think this one through….

Tony wanted a loan of $200. So they wanted him to write a check for $230, dated 2 weeks in advance. He can pay back the $230 or they’ll deposit his check. It’s only thirty bucks, Tony said. (Yeah, that’s why he’s broke.) But what kind of yearly interest are they charging?

The loan is for 2 weeks. There’s 52 weeks in a year. So the yearly interest rate is 26 times the percent interest he’s paying. (Get it? There’s 26 x 2 weeks in a year.)

Compare that to 20% yearly interest on a credit card.

He’s paying 230 bucks for a 200 loan. So he’s paying 30 bucks interest. Not cool. Cuz what percentage is that of 200 bucks? To figure it out, I take a short cut. See, 10% of 200 is 20 bucks. (200 x .1 = 20) So, I figure 5% (half of 10%) is 10 bucks (half of 20 bucks). That means 30 bucks is 10% plus 5%… 15%.

I can do all that in my head, see? But if you want to do the math, it’s like this:

30/200 = .15 or 15%

Fifteen percent interest don’t sound too bad, right? But that’s only for two weeks. To get yearly interest, you gotta multiply it by 26.

15% x 26 = 390%

Three hundred ninety percent! Almost 400% interest! I told Tony, you gotta get a credit card. You pay, what, 20% interest? Plus, if you pay it off when you get the bill in a few weeks, which is the smart thing to do, you don’t pay no interest at all. Just like a payday advance, but you’re payin’ nuthin!

Course, it’s dangerous to run up a big credit card bill. And Tony can’t trust himself. So I told him to get a card with a small limit, like $500. That’ll cover him for emergencies, right? Without him gettin’ ripped off too bad. He said, “I ain’t got no credit,” and I told him to call some credit card people. Try to get a card with no fees. Here’s some information I found. Some of it’s for college students, but hey, they’re in the same boat, just getting started with credit cards.

http://www.kiplinger.com/columns/drt/archive/2005/dt051013.html

http://www.youngmoney.com/credit_debt/credit_basics/041203

http://www.ftc.gov/bcp/conline/pubs/credit/choose.shtm

Just see what to do to get started, cuz what’s the point in paying all that extra interest?

Here’s something. This guy I know, Tony, he was strapped for cash. Had to make a car payment, and didn’t want his car repo-d. Yeah, we all been there. Best advice I give him is don’t spend all your dough and get into that situation. But, too late for that. You know how it is, everyone’s hard up.

He was gonna go to one of those payday advance loan places, and I said that’s no good. So let’s look at this. Here’s what they were offering:

Tony wanted a loan of$200. So they wanted him to write a check for $230, dated 2 weeks in advance. He can pay back the $230 or they’ll deposit his check. It’s only thirty bucks, Tony said. (Yeah, that’s why he’s broke.) But what kind of yearly interest are they charging?

The loan is for 2 weeks. There’s 52 weeks in a year. So the yearly interest rate is 26 times the percent interest he’s paying. (Get it? There’s 26 x 2 weeks in a year.)

Compare that to 20% yearly interest on a credit card.

Let me know how you figured out this comparison, and I’ll write later to tell you what I showed my friend.

What Percent OF the Original amount IS the Difference between the two amounts?

P × O = D

Percent decrease is pretty much the same thing. What percent of the original amount is the difference between the two amounts? Only difference in figuring it out is that the second amount is lower than the first, not higer. No sweat. The percent times the original amount still equals the difference. It’s just a decrease, not an increase. Get it?

Let’s look at it. Here’s a practice problem.

I filled up my car, so it had 15 gallons of gas in the tank. So, I drove out to my uncle’s house and back, and it took $18 in gas at $2 per gallon to fill up the tank. What was the percentage decrease in gas during the trip?

Did I get you with a tough one? More than jus’ one step here. Try to figure it out, then I’ll walk you through it…

Okay, here’s the deal. You need to do some steps to get the info you need to solve the problem… so what info do you need? Well, here’ s the formula we said….

P × O = D

Percent decrease (P) is what you’re tryin’ to find. Original value, you know that, it was 15 gallons, like the problem said.

P × 15 = D

But what’s the difference between the old amount of gas an’ the new one? Well, you gotta figure it out. It’s the amount of gas that got used, right? The info you have is that it took $18 at $2 per gallon to fill up the tank. How much gas can you get at $2 a gallon for 18 bucks? You know that, right? Divide 18 by 2, an’ you got 9 gallons. It took 9 gallons to fill up the tank, so the gas left at the end of the trip was 6 gallons. The difference between the 15 gallons started with an’ the 6 gallons ended with is 9 gallons. Get it?

P × 15 = 9

So, the percentage decrease is 9 divided by 15, or .6

P = 9 ÷ 15 = .6

Now, you gotta turn .6 into a percentage, an’ you jus’ move the decimal point over two to the right. So’s it’s 60%.

P = 9 ÷ 15 = .6 = 60%

The guy used 60% of his gas on the trip.

Knowin’ what a percent increase or decrease problem is askin’ is the big thing, and bein’ able to think through word problems. Let me know if you got any GED math that’s givin’ you a problem, an’ I’ll help you out.

For more information about the GED test and GED test preparation, visit the GED Academy at http://www.passGED.com.

I got a new hard drive, to back up my computer. The old hard drive I was usin’ was 250 GB. Now, the new one’s 640 GB. Sweet! So, what’s the percent increase in hard drive space from the old hard drive to the new one?

Give it a minute, try to work it out. What’dya think?

Here’s how I’d work through this one. First, you got to know what they mean when they say “what’s the percent increase?” It means, what PERCENT of the ORIGINAL AMOUNT is the DIFFERENCE BETWEEN (increase between) the two amounts. That’s puttin’ it in some context, right? First off, you got 3 important numbers. (1) PERCENT (P) = what you’re trying to find. (2) ORIGINAL (O) AMOUNT. (3) DIFFERENCE (D) BETWEEN old and new amounts.

Now, in math, “of” usually means “times.” And “is” usually means “equals.” So, I could put it like this.

P × O = D

What Percent OF the Original amount IS the Difference between the two amounts?

Well, you know the original amount. Dat’s my original hard drive size, 250 GB.

P × 250 = D

And to find the “difference” between two things, you gotta subtract. So the difference is the two amounts subtracted: 640 − 250 = 390

P × 250 = 390

To find P, the percent, you got to get P all by itself. So, to get rid of the “times 250,” you divide both sides by 250…

P × 250 ÷ 250 = 390 ÷ 250

P × 1 = 390 ÷ 250

P = 390 ÷ 250

P = 1.56

Now, P’s supposed to be a percent. To change a number to a percent, move the decimal place two to the right… the answer is:

156%

Let’s check it out… 100% bigger would mean it’s 250 GB bigger… one whole hard drive bigger. And it’s more than that. It’s more like 1-1/2 times bigger… that’s 150%. So the answer makes sense, right? Now, can you do the same thing with a percent decrease problem? What if it asked what the percent decrease was from 640 GB to 250 GB? Think about it, I’ll have a percent decrease problem in my next post….

Get that GED quick… you can do it!

For more information about the GED test and GED test preparation, visit The GED Academy at http://www.passGED.com.

Hi Curtis,

I need some help with percent and ratio word problems. Unfortunately your previous explanations regarding word problems have been too complicated. Perhaps you could give more information on the basics, the formulas? I know I am not completely understanding these formulas. My knowledge in math is only the basic concepts, and I do not understand algebra yet.

While percents seem simple enough; I become lost when I try to solve word problems with them. I have been using the triangle method to work with percent problems. [The method shown in the GED book.]

1- Multiply when the problem gives you the whole and the percent.

2- Divide when the problem gives you the part and the percent.

3- Divide when the problem gives you the whole and the part.

However, I am still finding word problems with percents and ratios very confusing, so I know I am definitely not understanding the formula. Ratios especially – the whole idea of cross multiplying sounds good, but when I do this I become lost as I attempt to finish the problem. I hope you can help me begin to make sense of these areas.

Thanks, Jen

Hey, Jen. The problem with percent and ratio word problems is, you gotta really think through what information they give you an’ how it relates to the problem they want you to solve. What are you actually tryin’ to find? How can you get it? It’s knowing when to use the different rules and formula’s that’s confusin’.

Like the triangle rules you said you use:

1- Multiply when the problem gives you the whole and the percent.

2- Divide when the problem gives you the part and the percent.

3- Divide when the problem gives you the whole and the part.

To use ‘em, you gotta know what ‘percent’ ‘whole’ an’ ‘part’ they mean. Here’s an example.

40 of the students in a class of 200 got B’s on their test. 10 got A’s, 2 got F’s, and 20 got D’s. What percentage of students got C’s?

What’s the whole, part, and percent?

The whole is the whole class: 200.

The percent is the percent of students got C’s. That’s what you’re looking for.

The “part” is the number of students that got C’s.

See, a “percent” is the fraction (or ratio) of the part to the whole. That’s all… it’s just a fraction, with the top divided by the bottom. So, 1/2 = 50% (1 divided by 2 = .5 = 50%) and 3/4 = 75% (3 divided by 4 = .75 = 75%). The part divided by the whole = the percent.

Part ÷ Whole = Percent

So, in a sense, a percent is the same thing as a fraction. 1/8 of a pizza is the part (1 piece) over the whole (8 pieces make a whole pizza). That same slice of pizza is 12.5% of the pizza, because 1 divided by 8 = .125 (12.5%).

All three of the “rules” come from the equation: Part ÷ Whole = Percent, just written in different ways.

1- Multiply when the problem gives you the whole and the percent. (Part = Percent x Whole)

2- Divide when the problem gives you the part and the percent. (Whole = Part ÷ Percent)

3- Divide when the problem gives you the whole and the part. (Percent = Part ÷ Whole)

All these formulas say the same thing… it’s just moving the three pieces of the formula around. So really, all you need to do is figure out what the question’s askin’, and find the other two numbers to plug into the formula.

Back to the word problem. It’s asking for a percent:

Percent = Part ÷ Whole

The “whole” is the whole class, 200 students.

Percent = Part ÷ 200

The “part” is trickier, cuz the word problem is really in 2 parts. The “part” is the number of students that got c’s. So, you need to subtract all the other students who got other grades from 200.

200 – 40 – 10 – 2 – 20 = 128

That’s the number to plug into the formula:

Percent = 128 (number of students with C’s) ÷ 200 (number of students in the class)

128 ÷ 200 = .64 = 64%

64% of students got C’s.

Okay, let’s try a ratio. A ratio is also sort of like a fraction, but it’s not necessarily the ratio of “part” to “whole.” A fraction is a ratio of “part” to “whole,” but a ratio is a ratio of anything to anything. In a speed problem, it can be a ratio of “miles” to “hours.” It’s anything that has a regular relationship. Okay, let’s try a ratio problem, and we’ll try an’ walk thru cross-multiplying.

A man works 8 hours per day in a factory, and he makes $20 per hour. In a 5-day workweek, how much does the man make?

Now, you might figure this out without even using a ratio. But it is a ratio… any time you see “per,” you can use a ratio. You need to figure out what’s equivalent to what. We’ve got some ratios:

8 hours : 1 day

That’s the same as 8 hours per day.

20 dollars : 1 hour

That’s the same as $20 per hour.

Now, if I want to find out how many dollars per day, I need to figure out the ratio of dollars to 8 hours. A ratio like this (something per something else) gives two things that are equivalent. 8 hours = 1 day, so a ratio of dollars per 8 hours will give us dollars per day.

20 dollars : 1 hour

x dollars : 8 hours

Now, I’ve got two ratios, with the same units, and they’ll be equal to each other. That gives me an equation:

20/1 = x/8

Now’s the time to cross multiply. Basically, cross multiplication is some simple algebra. It’s just a shorthand way to remember how to solve this kind of problem. To move numbers from one side of the equation to the other, you do the opposite operation. If one side is divided by a number (like 1), you can move that number to the other side of the equation by multiplying both sides by 1.

(20/1) x 1 = (x/8) x 1

The two ones on the left cancel each other out, and on the right you end up with x times 1 (or just x) over 8:

20 = x/8

Now, do the same thing with the 8:

20 x 8 = (x/8) x 8

The two 8′s cancel each other out, and 20 x 8 = 160:

160 = x

He makes $160 in a day.

160 dollars : 1 day

Now, how much does he make in 5 days?

y dollars : 5 days

It’s the exact same sort of problem. You can make an equation:

160/1 = y/5

Using the shorthand version of the math we did before, this is the same as 160 x 5 = 1 x y (cross multiplying)

160 x 5 = 1 x y

800 = y

That’s the answer: he makes $800 in a five-day workweek.

So, what you need to find out from a ratio problem is what ratio equals what other ratio. Then, you can cross-multiply to solve.

Hope this helps! If a practice problem is giving you problems, send it to me an’ I’ll walk thru it.

For more information about the GED test and GED test preparation, visit The GED Academy at http://www.passGED.com.

would like to know more about percentages. like dividing. here’s a question:

jacks auto service-summary of april sales activity

division …… april sales …… increase over march
parts ………. $11,000 ……… %10
services ….. $70,000 ……… %25

what was the combined sales revenue in march for the parts and services divisions of jacks auto service? answer is $66,000 how did they get that answer step by step?

Hey! Thanks for sendin’ in a math question. This is a good one. Percents is pretty tough for a lot of people. This one is a little harder than the one last week, cuz it’s got more steps. So let me walk through it….

The first thing I do is look through the problem to get all the information it gives. This one’s got the information in a chart, so that’s pretty easy, it’s all right there.

For parts, April sales = $11,000
April parts sales is 10% more than March sales.

For service, April sales = $70,000
April service sales is 25% more than March sales.

So, the second thing I look at is, what’s it askin’? What do they want to know? And that’s the combined sales (parts + service) for March. Course, the question don’t give you the March numbers, that’d be too easy. Question is, how do you find the march numbers?

Well, let’s take parts first. I’m gonna call March parts sales P, just to have something to stand for it. April parts sales ($11,000) is (equals) 10% (10% times P, cuz they mean 10% of March parts sales) more than (plus) March part sales (P). So,

$11,000 = (10% x P) + P

Now, you gotta find P. With percent problems, first thing I always do is change the percent to a decimal, that’s just moving the decimal point 2 places to the left. So, 10% = .1 (if there’s no decimal already, it’s at the end of the number). So,

$11,000 = .1P + P

Now, a P by itself is 1P, so .1P plus P = 1.1P

$11,000 = 1.1P

So, I divide $11,000 by 1.1 to get P by itself.

$11,000/1.1 = P

That’s the same as dividing $110,000 by 11 (You can move the decimal point over one in the 1.1, as long as you move it over one space in the 11,000, too.):

$110,000/11 = P

And that’s $10,000 (11 into 11 once, then all that’s left is zeros…)

$10,000 = P

So, does it make sense? If you think about it, 10% of $10,000 is $1,000, and so $11,000 is 10% higher than $10,000. Makes sense to me!

Now, do the exact same thing for service sales, S, with the numbers for service. See how the equation is the same?

$70,000 = (25% x S) + S
$70,000 = .25S + S
$70,000 = 1.25S
$70,000/1.25 = S
$7,000,000/125 = S
$56,000 = S

So, now you know that for March, Parts sales were $10,000, and Service sales were $56,000. Add ‘em up, an’ you get $66,000 total sales….there ya’ go! So:

1) Get your info together.
2) Figure out what the questions askin’.
3) Make an equation to figure out the answer.
4) Solve step-by-step.

Special advice for percents:
For percents, change ‘em to decimals by moving the decimal two places to the left. Do this right away!

Also, when they say “something-percent more than another number”, that means “something-percent TIMES the original number PLUS the original number”

“something-percent less than another number” means “the original number minus something-percent TIMES the original number”… So, if $9,000 is 10% less than X, $9,000 = x – (.1x), so $9,000 = 1x – .1x = .9x …. x = $9,000/.9 = $10,000

Hope this helps!
Curtis

For more information about the GED test or GED test preparation, visit The GED Academy at http://www.passged.com

Look my only problem with this whole G.E.D test are the word problems that involve measurements and precentages….. They stump me really bad and I just get so frustrated and give up on it…I need some advice on how to solve these problems…They really confuse me and the more and more I try the more frustrated I get at myself cause I just cannont solve them….If someone could give me some advice it would be much appreciated. Thanks -Kandyce

Hey, Kandyce. The GED has all kindsa word problems. So, the first thing is figurin’ out what they’re asking, then doin the math. Of course. Measurements and percentages is actually a lot of stuff, but let me walk thru a couple of examples, and if you have some other problems you’re havin’ trouble with, send ‘em to me, and I’ll work them out to show you how I did it.

Okay, here’s an example problem with percents, like you might get on the GED.

A bookcase is on sale for $440. The sale is 20% off the regular price. What is the regular price of the bookcase?

So, I look at a problem like this, an’ I got to figure out what it’s askin’ for. Can’t do the math if you don’t know what math it wants you to do! So, I start by takin’ the information out of the problem. There’s a sale price…It also says the sale is 20% off. So that’s the information I got to work with:

Sale price = $440

Sale = 20% off

So, the next step is to ask what’s it askin’? It’s askin’ for the regular price. That’s what I’m trying to find, so I’ll call it “x”.

Sale price = $440

Sale = 20% off

Regular price = x

Now, how do I make this stuff into an equation I can solve? How are these numbers related to each other? Cuz that’s what an equation is, it tells the relationships between different numbers.

How do you get the sale price from a regular price? Well, first you’ve got to figure what amount is the percent off, then subtract that from the regular price, right? So, if it’s $100 and it’s 20% off, then 20% of (times) $100 = $20, and $100 – $20 is $80… so the sale price is $80. So, I need to put that relationship in an equation…with “x” for the regular price.

x – (x × 20%) = $440

Yikes! That looks like a pain to solve. So, is there any easier way to think of it? Well, if the sale is 20% off the original, then the sale price is really 80% of the original price, right? I mean, if you take away 20% from any number, what have you got left? 80% of the original number. So, another way to say x – (x × 20%) is x × 80%.

On the test, use your common sense to try to put things the easiest way! But for now, let’s figure that out with math, so you can see it’s true. The first thing I’m gonna do is change 20% to .2 Remember, to change a percent to a decimal, just move the decimal place over two to the left, so 20.0% = .200 or just plain .2

x – (x × 20%) = x – (x × .20)

And x × .20 = .2x, since if you’re multiplying a number by a variable, just put the number and variable next to each other. Easy.

x – (x × 20%) = x – (x × .20) = x – .2x

And how do you subtract? Well, x is really 1 times x. So you subtract .2 from 1 and get… .8x Yes, that’s the same as 80% of x.

x – (x × 20%) = x – (x × .20) = x – .2x = 1x – .2x = .8x, or 80% of x

But you can use your common sense. If something’s 20% off, the sale price is 80% of the original. If it’s 15% off, the sale price is 85% of the original. If it’s 30% off, the sale price is 70% of the original. So, the sale price ($440) is 80% of (times) x.

.8x = $440

Now, that’s not too hard. x = $440 divided by .8, or $4400 divided by 8.

x = $440/.8 = $4400/8 = $550

That’s not too hard… 8 into 40 is 5…then 8 into 40 again is 5… with 0 left at the end. $550 is the answer.

Did you follow all that? It’s easy to get mixed up with those word problems, you just got to think them through…really figure out what they’re askin’. Here’s a website where you can practice more percent problems:

http://www.saab.org/mathdrills/percent.cgi

Okay, here’s one with measurements. Here’s the trick with measurement…stuff’s not always in the same type of measure! Yo, you know they tryin’ to trick you with that stuff. So, you get a problem like this:

Joe is out in the park practicing hitting a baseball. He’s aiming at a tree 120 yards away. He hits the ball 50 yards, 5 feet, 3 inches. He hits another ball 62 yards, 8 feet, 6 inches. In feet, how much closer is his second ball to his goal than the first ball?

Okay, feet, yards inches. Three different kinds of measurements! Yuck. But you gotta deal with it, y’know? Okay, so I start the same way, what info do I got?

tree = 120 yards

ball 1 = 50 yards, 5 feet, 3 inches

ball 2 = 62 yards, 8 feet, 6 inches

First thing I’m gonna do is change everything to feet. That’s what the answer wants, it says “IN FEET,” so if I change everything to feet now, it’s not gonna screw me up later. Seriously, if you remember one thing about measurement word problems, make it to CHANGE ALL MEASUREMENTS TO WHAT YOU WANT YOUR ANSWER IN FIRST THING.

A yard = 3 feet, so yards I multiply by 3.

tree = 120 yards = 360 feet

ball 1 = 50 yards, 5 feet, 3 inches = 150 feet + 5 feet + 3 inches = 155 feet, 3 inches

ball 2 = 62 yards, 8 feet, 6 inches = 186 feet + 8 feet + 6 inches = 194 feet, 6 inches

Now, I got to change inches to fractions of a foot. Since one foot is 12 inches, I divide the number of inches by 12.

tree = 360 feet
ball 1 = 155 feet, 3 inches = 155 feet + 3/12 feet = 155 feet + 1/4 feet = 155-1/4 feet

ball 2 = 194 feet, 6 inches = 194 feet + 6/12 feet = 194 feet + 1/2 feet = 194-1/2 feet

Now we’re getting somewhere. But I got to go back and ask the big question: what exactly do they want to know? They want to know how much CLOSER the second ball is. This is about COMPARING THE LENGTHS. That is, what’s the difference between the first ball and the second ball? Heck, I don’t even need to know the distance of the tree. I just got to subtract…

Distance closer = ball 2 – ball 1

Distance closer = 194-1/2 feet – 155-1/4 feet = 39-1/4 feet

That’s the answer! Pretty easy, once you get it all in feet and figure out what they want. Now, there’s lots of types of measurements, and knowing how to change (or convert, as they say in math) one type of measurement like yards into another like feet is important. So, here’s some websites to help with that:

http://www.mathleague.com/help/metric/metric.htm

http://www.quiz-tree.com/Units_of_Measurement_main.html

http://www.mce.k12tn.net/measurement/measurement_chart.htm

Hope this helps! Good luck gettin’ that GED. Seriously, you can pass the GED math test!

For more information about the GED test and GED test preparation, visit The GED Academy at http://www.passGED.com.