Ah, great question! This is one of my favorite topics...so many sentences actually embed the equation right in them, and it comes down to the "language of mathematics":
These words translate directly into symbols:
Is (or any form of "to be") --> =
Of --> * (multiplication)
Per --> / (division)
Greater than --> > (in an inequality) or + (in an equation)
What --> x (your variable)
So...if a sentence says:
What is 20% of 15?
You can directly translate that to:
x = 20/100 * 15
x = 1/5 *15
x = 3
Or if it asks:
15 is what percent of 75?
That translates to:
15 = x/100 * 75
15 = 3/4 x
x = 20
The key with percents is that the percentage must be taken "of" something, so if it asks:
What is 30% greater than 40?
Then you have to determine what the % change is in terms of. Here, you'd increase 40 by a percentage of itself:
x = 30/100 * 40 + 40
x = 1200/100 + 40
x = 52
To me, the important terms in these words-to-equations are usually "is" and "of". "Is" sets up your equation, and when fractions or proportions are present that word "of" may be inferred ("of itself"), so you'll need to be careful about that. but try this on a set of word problems and I think it will give you a great start...
Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep
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