You know the old math class argument we all attempted to use to get out of learning the quadratic equation, sine and cosine, and symbolic functions: "When am I ever going to use this in the real world?" I've been existing in that real world for a good chunk of time now, and aside from my paid gig as a test prep writer, I can honestly tell you the answer to that question for me has been "Never." But there is one content area on the ACT and SAT that I encounter almost weekly: percentages. They are everywhere in the real world, from restaurant tips to clearance sales to tax payments, which is probably why they are so prevalent on the ACT and SAT. But have no fear of percentage problems: nearly all of them can be tackled quickly with a little translation, a strategy that I guarantee you will use on the test and in the real world.
If you view Math as a language, you'll quickly realize that it has symbols that can be translated into English and that English can in turn be translated into Math. Students often struggle with percentage problems written in English, but they are easy to solve if you use translation: to do this, convert words to math symbols and then break down the question phrase by phrase.
Let’s consider an example:
If 10 is 2% of z, what is 50% of z ?
Start with the first part of the question—if 10 is 2% of z—and translate it into math symbols. Think back to what you know about the basics of translation:
of = multiply
is = equals
Every time you see the word “of” in your problem, use a multiplication sign (x).
Every time you see the word “is” use an equals sign (=).
if 10 is 2% of z
10 = 0.02 x z
You now have a mathematical sentence, and can solve for z:
10 = 0.02 x z
10/0.02 = (0.02 x z)/0.02
500 = z
Some students stop here and select answer choice (D). Wrong answer! Remember, we have only translated the first half of the question. It is wise to reread the question when you believe you are finished to make sure you completed the entire problem. The test makers will have answer traps for those who only complete part of the question.
Now you must attack the second part—what is 50% of z ? Another basic translation code is the word what. If there is no x variable in the problem, you can make what = x. But if x is already used, then you must give what another symbol. We recommend using a question mark to avoid confusion. For example:
what is 50% of z
? = 0.50 x z
In the first part of the question, we found that z = 500. Using this information, solve for the question mark:
? = 0.50 x 500
? = 250
The correct answer is (C), 250.
Most percentage problems like this one are considered among the easiest difficulty level. However, the test makers can boost the difficulty by changing what to what percent in a word problem. Whereas what = ?, what percent = ?/100. If you can remember this simple translation, you can easily score points on more difficult questions.
Let’s examine a higher difficulty level question using what percent:
Don’t let the expression in terms of s throw you; this simply means that s will appear in the answer choices. We recommend that you cross this phrase out so that you are left with what percent of t is 100.
As with the previous problem, let’s start with the first half of the question:
s is 2% of t
s = 0.02 x t
Since we are solving in terms of s, find t:
Now move to the second half of the question. Remember to use ?/100 when translating what percent.
And now solve for the question mark:
The correct answer is (E).
Translation is a good solution strategy for students who find percentage word problems confusing or worrisome. Remember to use a multiplication sign for of and ?/100 for what percent.
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