Page 157 - ArithBook5thEd ~ BCC

The statement “A is P percent of B”is equivalent tothe proportion

A P
= .
B 100

The letter B is used to suggest “base amount” – that is, B is the amount from which (or of which)
a percentage is taken. Notice that B follows “of” in the verbal statement. It could be that A (the
percentage taken) is greater than B, but only if the percentage P is greater than 100.
In the following examples, the phrase involving “what,” as in “what number?” or “what percent?”
helps determine which of A, B of P is the unknown.

Example 195. 6 is what percent of 300?

Solution. The percent is unknown, and the base amount B is 300 (since it follows the word “of”). We
can restate the question as: “6 is P percent of 300.” The corresponding proportion is

6 P
=
300 100
and the solution (verify it!) is P = 2. Therefore, 6 is 2% of 300.

Example 196. What number is 8% of 150?

Solution. The base amount B is 150, since it follows the word “of,” the percentage is P = 8, and there-
fore A is the unknown amount. The question can be restated as: “A is 8% of 150.” The corresponding
proportion is
A 8
=
150 100
and the solution is A = 12 (verify!). It follows that 12 is 8% of 150.
(Note that this result could have been obtained without using a proportion, since 8% of 150 simply
means .08 × 150 = 12.)

Example 197. 58% of what number is 290?

Solution. The base amount B is unknown, and A is 290. The question can be restated as “58% of B
is 290.” The corresponding proportion is
290 58
=
B 100
and the solution is 29000 =500. So 58% of 500 is 290.
58
Everyday questions involving percent are not always as straightforward as in the previous examples.
But with a little thought, they can be converted into such statements.

Example 198. Approximately 55% of the students enrolled at BCC are female. If there are 2970 female
students, what is the total enrollment at BCC?

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