GED Math: Word Problems with Measurements and Percentages

Here’s a comment from Kandyce about the GED math test, let’s see if I can help:

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.