There are a lot of percent questions on the ACT Math® section. They really like to ask this sort of question. Fortunately, percents are pretty straightforward. They also have applications in real life, such as paying tax or a tip.
What Are Percents?
Percent comes from the Latin "per 100". So when we're asking what 20 percent of 100 is, we're just asking how much of 100 is contained in 20? It's circular. 20%.
This becomes trickier when the ACT Math® gives you non-100s to work with. Consider what is 120% of 100? Okay, so what is not only 100% of 100, but what is 20% more? 20% more is 20, so 120% of 100 is 120. Pretty straightforward still.
What about 80% of 120? Should be 100 right? Put it in your calculator.
It's not. That's not how percents work. The ACT Math® section often challenges students with this type of question.
How to Solve Percent Problems
Percents are pretty straightforward. You just have to convert each percent to a number out of 100. So 20% out of 100 is two decimal places to the left. So 0.2.
Let's Practice
Example 1:
What is 30% of 50?
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To solve this, just move the decimal point two places to the left: 30% becomes 0.30. Then multiply:
That's it!
Example 2:
If a $80 shirt is on sale for 25% off, what's the sale price?
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First, find 25% of $80:
This is how much you're saving. Now just subtract that from the original price:
The sale price is $60.
Common ACT Math® Percent Challenges
The real tricky application of this is going to be with 5%. Many students miswrite this as 0.5 – that's 50%! 5% is actually 0.05.
You'll also see percent increase and decrease problems.A 100% increase doubles the original amount, while a 100% decrease reduces it to zero.
Practice Section
Let's try some ACT®-style questions:
Question 1:
A store increases the price of a sweater by 20%. If the new price is $72, what was the original price?
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Answer: $60
Explanation:
Let's work backwards. If the price increased by 20%, that means the new price is 120% of the original. So, $72 is 120% of the original price. We can set up this equation:
Solving for x:
Therefore, the original price was $60.
Question 2:
In a class of 30 students, 40% are boys. How many girls are in the class?
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Answer: 18 girls
Explanation:
If 40% are boys, then:
$0.40 \times 30 = 12 \text boys$
So, the number of girls = Total students - Number of boys
Question 3:
If 85% of students passed a test, and 102 students passed, how many students took the test?
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Answer: 120 students
Explanation:
Let x be the total number of students.
$85% {' '}\text of {' '} x = 102$
So, 120 students took the test.
Conclusion
Remember, the more percent problems you solve, the more comfortable you'll become with them.