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How to Solve Complex Percent Problems on the ACT

Using your calculator to find a result on the ACT is straightforward when you know the number you’re calculating with and the percentage you’re taking. However, some math questions on the ACT will involve complex percent problems that will be challenging to solve, even with a calculator.

When answering a question that involves percentages, the trick is to translate it into an equation. Substitute either 0.01 or

image0.png

for the percent sign, and let x (or any variable you like) stand for the number you’re trying to find. Then use algebra to solve for x.

Here are two examples of practice problems you may see on the ACT.

Example 1

What percent of 600 is 270?

image1.png

A good way to solve this type of percent problem is to translate the words into an equation. Here’s how the example problem would look:

image2.png

Substitute 0.01 for the percent sign in this equation and solve for x:

image3.png

Thus, 45 percent of 600 is 270, so the correct answer is Choice (C).

Example 2

If 40 percent of a is 30, then a is what percent of 50?

image4.png

To answer this question, you first need to find the value of a, so make an equation from the values in the first part of the question. Here’s how it would look:

image5.png

Now solve this equation for a:

image6.png

Thus, a = 75. Finally, you make an equation from the values in the second part of the question. Here’s how: “75 is what percent of 50” becomes

image7.png

Substitute 0.01 for the percent sign in this equation and solve for x:

image8.png

So the correct answer is Choice (K).

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