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.

Hey there! Algebra’s got a lot of stuff in it, and it takes a while to learn. You can look at a lot of the algebra articles here: http://www.passged.com/student_blogs/curtis/category/algebra/. Here’s the absolute, need-to-know’s:

1) Gotta understand the idea of a variable. A variable is a letter or symbol that stands for something unknown or something that can change. A lot of the time, you’ll see “x” used as a variable: x + 5 = 10 … why do you use a variable? Cuz you want to figure something out, and to put the “something you don’t know” into a math equation you need some sort of symbol for it. That’s where the x comes in. You’ll need to be able to understand what 2x means (2 times x) and mutliply, add, and subtract with variables to move them around.

2) Gotta understand how to move numbers around in an equation. In an equation, you can add the same number to both sides, subtract the same number from both sides, multiply both sides by the same number, or divide both sides by the same number (as long as it’s not zero). Why do you want to do that? So you can move all the numbers to one side, and the variable to the other, and figure out what the variable equals. So, for x + 5 = 10, you can subtract 5 from each side. Then, x = 5. Easy.

3) Gotta be able to see what an equation means in real life. So, take a word problem and make an equation out of it.

4) Understand inequalities, like 4 < 2x or x +5 > 10.

5) Gotta know how to deal with negative numbers and fractions. Why? These are the main things that’ll mess you up in moving around numbers. Better you understand them, the better you’ll do.

6) Helps to know about exponents, like x². You won’t get into real high exponents, jus’ understand what “squared” means (something times itself) and what a square root means.

7) Helps to know about graphing a line… like what’s a slope? How do you get a line on a graph from an equation?
The hardest part is quadratic equations (you can see my article ’bout them). But there’s not gonna be a lot about them on the GED, so no big sweat.

Dat’s the basics. I know it’s a lot, an’ I can’t promise my website covers it all. But your son can always write in to me with special problems if he’s havin’ trouble with something. It’s hard to study on your own, so I totally recommend the GED Academy study program at http://www.passGED.com. It’s got a real complete math course, and if he has a problem he can call up an instructor for help.

If x= y-3 and y=z^2, what is x in terms of z?

That caret, that’s shorthand for “to the power of.” So I’m gonna state it:

x = y – 3

y=z²

What you want to get is x in terms of z. Well. This ain’t really too hard. It’s just figurin’ out how to make x equal to a bit of math with a z in it instead of a bit of math with a y in it. You know what x means in terms of y. It’s y – 3. And you know what y means in terms of z. The key is, with any type of algebra, if two things are equal, you can substitute one for the other. So, since z² is equal to y, you can put it into the first equation instead of y. So:

x = z² – 3

That’s all you need to do! That’s x in terms of z. You can’t really reduce it any, and it’s what the question asked for. It just asks you to understand that, if two things are equal, you can substitute one for the other.

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

]]> http://www.passged.com/student_blogs/curtis/2009/01/22/some-advanced-algebra-but-not-too-hard/feed/ 0 http://www.passged.com/student_blogs/curtis/2009/01/22/ged-math-algebra/ http://www.passged.com/student_blogs/curtis/2009/01/22/ged-math-algebra/#comments Thu, 22 Jan 2009 17:49:57 +0000 Curtis http://www.passged.com/student_blogs/curtis/?p=74 Here’s a problem that Lyndia sent in, since she was havin’ trouble with it:

3x = 7 – 4x

You wanna figure out what “x” is equal to The problem comes in when you have a number befo’ the x, and need to get all the “x”es on the same side. Think of it this way… you don’t just got one x, you got four x’s. So, you gotta move all 4 x’s to the other side. In other words, think of “4x” as all going together.

3x = 7 – 4x

Add 4x to both sides to get rid of the x’s on the right…because you have to get rid of all four x’s.

3x + 4x = 7 – 4x + 4x

The -4x and the +4x cancel each other on the right side… and on the left, 3x + 4x = 7x. Think of it like that’s how many x’s you got… 3 x’s (x +  x + x) plus 4 x’s (x + x + x + x) gives you 7 x’s (x + x + x + x + x + x + x).

7x = 7

Now, if the 7 goes with the x, how do you get rid of it? You can, because what it’s really saying is 7 times x. 7 times x is the same as (x + x + x + x + x + x + x) is the same as 7x. Just like 7 times 3 is the same as (3 + 3 + 3 + 3 + 3 + 3 + 3), and could be written 7(3). Divide by 7 on both sides to get:

x = 1

Let me know if this gives you any more problems!

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

So, let’s try walkin’ thru one.

Jerry wants to buy twelve pizzas. The pizza place has a discount special, where you buy 2  pizzas and get the third 1/2 off. If P is the price of a pizza, which formula shows the price of twelve pizzas?

A) 12P/2 + 2P

B) 1/2 x 12P

C) 12P – .5P

D) 8P + .5(4P)

Okay, so what do these formulas really mean? Let’s work it from the formulas, to see if they match up with the question.  P is the price of pizzas. So, the first formula means:

12P/2 + 2P means 12 pizzas, divided by 2, plus 2 pizzas. So, twelve pizzas are half off (that’s the divided by 2), and 2 pizzas are full price. That ain’t right. He’s buyin’ twelve pizzas, not 14, and he’s not gonna get half off of 12 of them.

Let’s try the next one. 1/2 x 12P means 1/2 off of 12 pizzas. Well, that’s not right. Only every third pizza is half off.

How ’bout the next one?  12P – .5P means twelve pizzas minus the price of half a pizza. That’s only one pizza being half off. That’s not right. He oughtta have more than that off his total.

Only one left.  8P + .5(4P) means 8 pizzas plus half of 4 pizzas. Point-five means half just like a fraction. So, is that right? If it’s buy 2 get 1 half off, there should be twice as many full price pizzas as half price pizzas. So there are. 8 is twice 4. So for every 2 full-price pizza, he pays half for one other pizza. And there should be 12 pizzas all together. And there are. 8 pizzas and 4 half-price pizzas, that’s 12. There’s your answer.

Let me know if you’ve got any questions.

For more information about the GED test and GED test preparation, visit The GED Academy at http://www.passGED.com or call 1-888-880-2164.

hi im austin.
i have a question on some things. im having trouble with the quadratic equations and graphs. the quadratic equation i just cant seem to understand quite that well. The graphs…well i just cant figure out how to solve the slop of a line and everything else. You think you could maybe give me some good advice on an easy way to understand everything about quadratic equations and x and y axis graphs.

Part 1: Quadratic Equations for the GED

Yeah, this is the hard stuff. Quadratic equations… the good news is, you won’t have a lot of them on the GED test. The first thing is, what is a quadratic equation, anyway? It’s an equation with x squared in it, basically. Usually, it has something x squared, plus or minus something x, plus or minus a number, equals something. Like: x² + 3x – 4 = 0

Quadratic equations are hard to solve. I’m just gonna deal with the easier ones, those’ll be the kind on the GED. That means, there’s no number before the x squared. When you get an answer, there’s gonna be two possible numbers for x, because of the square. That’s because a square root can be negative or positive. So -1 squared is 1, and 1 squared is also 1.

There’s a big, confusing formula for finding x in a quadratic equation like this one. But there’s also a shortcut. The best way to solve these (the simple ones, that is, which are the ones on the GED), is to factor. That just means, find two things that multiply together to equal the equation. To do this, you’ve kind of got to work backwards. Your factors are going to look like this: (x + ?) (x + !) = 0. Remember, the question mark and exclamation mark can be negative or positive numbers.

If you multiply out (x + ?) and (x + !) you get x² + (! + ?)x + (! times ?).

It don’t matter what the numbers are… the number by the x is going to be your two numbers added together, and the number without the x is going to be the two numbers multiplied together. So, if the example is this: x² + 3x – 4 = 0, what two numbers can multiply together to get -4? (You take the minus sign and put it with the 4. That’s the big stumbling block…) You can multiply 4 times -1, or -4 times 1, or 2 times -2.

So, which of those, added together equals the middle number, +3? It’s 4 and -1. So, x² + 3x – 4 = (x + 4) (x + -1)

So, (x + 4) (x + -1) = 0. That means, either x + 4 or x + -1 will equal 0. The possible answers for x are -4 and 1, the opposite signs of your numbers. Did you follow all that?

On the GED, it can be easier to try the answer choices in the equation, to see which ones are right. For more about quadratic equations, check out:

http://www.themathpage.com/alg/quadratic-equations.htm

http://www.purplemath.com/modules/quadform.htm

http://plus.maths.org/issue29/features/quadratic/index-gifd.html

Part 2: Graphs for the GED

x and y axis graphs… well, here’s the deal. Any kind of equation with two variables (an x and a y) can be graphed as a line. Lines’ll have different shapes, depending on the equation. You’re really askin’ about graphs of lines. That means, there’s no squares or anything funny in the equation. There’s an x and a y, and the line is made up of all the possible numbers for x and y that can make the equation true.

For x = y, the numbers for x and y will always be the same. So, if x =1, then y = 1. If x = 2, y = 2. The line will be a straight line on a graph where all the x’s equal all the y’s. Okay, it’s easier to look at it. Go here to get a great intro to graphing lines:

http://library.thinkquest.org/20991/prealg/graph.html

So, you asked about slopes. That means, how steep is the line on the graph, and what direction does it go? So, the slope’s got two parts, and the answer to those questions is put into a number.

First, how steep is the line? You can figure it out by picking two points on the line, and seeing how far UP and then how far OVER you’ve gotta go to get from the first point to the second. Divide how far you went UP by how far you went OVER. That gives you a number.

Then, which direction is it going? Going from bottom to top, does it lean to the right? Then the slope’s a positive number. Does it lean to the left? Then the slope’s a negative number. Here’s a link you can go to to practice finding the slopes of some lines.

Slope Practice Worksheet: http://www.algebrahelp.com/worksheets/view/graphing/slope.quiz

Also, check out more about graphing here: http://library.thinkquest.org/20991/alg2/graphs.html

You can also figure out the slope just from an equation, if it’s said in a particular way, called Slope Intercept form. Slope Intercept form has the number for the slope in it, and the number for the y-intercept (where the line passes through the y axis, or where x=0). It goes like this: y = mx + b

m = slope, and b = y-intercept

So, if your equation is y = 2x + 3, then the slope is 2. Makes it easy to find, huh?

Here’s a cool page lettin’ you see how the Slope Intercept form looks like as a line:

http://id.mind.net/~zona/mmts/functionInstitute/linearFunctions/lsif.html

Here’s some practice making lines using Slope Intercept form:

http://www.algebrahelp.com/worksheets/view/graphing/slopeintercept.quiz

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

AlgebraHelp.com has lessons, worksheets, and a calculator to help you out: http://www.algebrahelp.com/

This site’s got basic math and pre-algebra, so it’s good if you need to build up some basic math skills before tackling the algebra: http://home.earthlink.net/~djbach/basic.html#anchor988522

Purplemath has a whole lot of explanations of algebra ideas, starting with the basics. http://www.purplemath.com/modules/index.htm

Help Algebra has nine chapters, like a math book, explaining algebra: http://www.helpalgebra.com/

Hmmmm…. I gotta study some of these things myself. What’s giving you a headache on your GED? Let me know, and I’ll try to figure out a good answer for you. You know, make it real. Just leave a comment, and I’ll get you a GED-rockin’ answer.

To find out more about the GED test and GED test preparation, visit The GED Academy at passGED.com.

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.