# How To Solve Percent Problems Using Proportions

We often get reports about how much something has increased or decreased as a percent of change.The percent of change tells us how much something has changed in comparison to the original number.

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Jeff has a coupon at the Guitar Store for 15% off any purchase of $100 or more. He wants to buy a used guitar that has a price tag of$220 on it.

$$\frac= \frac$$ $$\frac\cdot = \frac\cdot 8$$ $$2\cdot 100= \frac\cdot$$ $$\frac=\frac$$ $$x=25\%$$ This proportion is called the percent proportion.

$$\frac=\frac$$ Fractions, percent and decimals can all represent the same number, but they are expressed differently.

Example Use cross product to determine if the two ratios form a proportion.

## How To Solve Percent Problems Using Proportions

$$\frac,\: \: \frac$$ $$\frac\overset \frac$$ $$\frac\cdot 16\cdot 40\overset \frac\cdot 16\cdot 40$$ $$\frac\cdot\cdot 40\overset \frac\cdot 16\cdot$$ \$\cdot 40\overset5\cdot 16$$=80$$ Here we can see that 2/16 and 5/40 are proportions since their cross products are equal.

To solve problems with percent we use the percent proportion shown in "Proportions and percent".

$$\frac=\frac$$ $$\frac\cdot =\frac\cdot b$$ $$a=\frac\cdot b$$ x/100 is called the rate.

Jeff wonders how much money the coupon will take off the original 0 price.

In a percent problem, the base represents how much should be considered 100% (the whole); in exponents, the base is the value that is raised to a power when a number is written in exponential notation. Since the percent is the percent off, the amount will be the amount off of the price.

## Comments How To Solve Percent Problems Using Proportions

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