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Increasing/Decreasing by a Percent - 5

Many problems require the student to use common sense to solve them—that is, mathematical reasoning. For instance, when a problem refers to consecutive integers, the student is expected to realize that any two consecutive integers differ by one. If two numbers are consecutive, normally x is set equal to the first and x + 1, the second.

Increasing/Decreasing by a Percent - 4

A box has a square bottom. The height has not yet been determined, but the bottom is 10 inches by 10 inches. The volume formula is V = lwh, because each of the length and width is 10, lw becomes 10 – 10 = 100.

Increasing/Decreasing by a Percent - 3

For some word problems, nothing more will be required of you than to substitute a given value into a formula, which is either given to you or is readily available. The most difficult part of these problems will be to decide which variable the given quantity will be. For example, the formula might look like R = 8q and the value given to you is 440. Is R = 440 or is q = 440? The answer lies in the way the variables are described In R ¼ 8q, it might be that R represents revenue (in dollars) and q represents quantity (in units) sold of some item. ‘‘If 440 units were sold, what is the revenue?’’ Here 440 is q. You would then solve R = 8(440). ‘‘If the revenue is $440, how many units were sold?’’ Here 440 is R, and you would solve 440 = 8q.

Increasing/Decreasing by a Percent - 2

At times the percent is the unknown. You are given two quantities and are asked what percent of one is of the other. Let x represent the percent as a decimal number.

Increasing/Decreasing by a Percent - 1

Many word problems involving percents fit the above model—that is, a quantity being increased or decreased. Often you can solve these problems using one of the following formats: