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Solution. According to the given information, 2970 is 55% of the total enrollment, which is the base
amount, B. The question can be restated as “2970 is 55% of B” and the corresponding proportion is
therefore
2970 55
= .
B 100
Using lowest terms of the fraction 55 = 11 ,we solve
100 20
2970 11
=
B 20
59400 = 11B
59400
B = =5400.
11
The total enrollment is 5400 students. To check, verify that 55%of 5400 is 2970.

Example 199. Full-time tuition at a university increased from $2, 850 to $3, 000. What was the percent
increase in the tuition? (Round to the nearest tenth of a percent.)

Solution. The tuition increased by $3000 − 2850 = $150. The percent increase is the ratio
amount of increase 150
= ,
original tuition 2850

expressed as a percent. Equivalently, we want to answer the question “$150 is what percent of $2850?”
We solve the proportion
150 P
= (5.1)
2850 100
3 P
=
57 100
57P =300
P ≈ 5.26

Rounded to the nearest tenth of a percent, the tuition increase was approximately 5.3%.

5.3.1 Exercises

1. 12 is 20% of what number?
2. 12 is 30% of what number?

3. 12 is 40% of what number?

4. 90 is what percent of 225?

5. 90 is what percent of 300?

6. 90 is what percent of 375?
7. What is 125% of 600?

8. What is 175% of 600?

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