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By definition, the word percent means "part of 100." On a practical basis, 20% means 20 out of 100, or 20/100, or 0.20. In SAT, word problems, you will need to convert numbers from fractions and decimals to percent (and vice versa). You will also be expected to use percents in practical situations, such as taxes, sales commissions, and price increases (and reductions). In most cases, they can easily be solved using the standard formula: Percent = Base x Rate

Example 1: Finding the Original Whole

After a 65 percent increase, the student body at Brandywine College was 15,860. How many students were enrolled at the college before the increase?

a.	5,551
b.	7,920
c.	9,612
d.	10,309
e.	21,411

Solution: There isn't anything terribly difficult about this question, IF you understand how to work with percentages. In this case, we can simply "convert" the information we are given into an easy and straightforward formula.

First, we must define our variable X as the unknown quantity, which is the original enrollment at the college. According to the question stem, the total number of students (15,860) is 65% higher than the original number. Hence, 15,860 = 1.65X.

If we solve for X, we find that the original number of students was 15,860/1.65 = 9,612. Choice C is correct.

Alternatively, we can solve this problem using the basic equation Percent = Part X Whole. In this case, however, the unknown X is the Part, and the new enrollment (15,860) is the Whole. Our equation becomes: 165% = Part X 15,860. When we solve it, we find that the Part, which is the original number of students, is 9,612.

Example 2. Combining Populations with Different Percentages

In a college lecture hall, 60% of the students have tattoos. In a second class that is twice the size of the first, 20% of the students have tattoos. What percent of both classes are students without tattoos?

a.	30%
b.	33-1/3%
c.	40%
d.	50%
e.	66-2/3%

Solution: This problem is tricky because it gives percentages, but no actual numbers. It also combines two populations of different sizes into a single whole. Finally, it asks for the percentage of students without tattoos (rather than with them), which adds an additional level of difficulty.

To solve, we must plug in random numbers for the class sizes and solve for the percentage. Then, we will combine the values into a single total. Let's assume that the first class has 100 students.

First class = 100. 60% = 60 students with tattoos
Therefore, the second class = 200. 20% of 200 = 40 students with tattoos

Now, we must combine these numbers to find the % of students with (and without tatoos) in the entire group:

(60 + 40)/300 = 100/300 = 33-1/3% of the students have tattoos. Therefore, the percentage without them is 66 -2/3%. Choice E is correct.

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