# Problems involving percent increase and decrease

Want more practice with percents and related concepts?

- Changing Decimals to Percents
- Changing Percents to Decimals
- Writing Expressions Involving Percent Increase and Decrease
- Calculating Percent Increase and Decrease
- More Problems Involving Percent Increase and Decrease

Here, you will practice solving problems involving percent increase and decrease. You may use a calculator for these exercises.

## Examples

$$\cssId{s8}{(0.7)(1.19)(\$50) = \$41.65}$$

Why?
To increase *any* amount by
$\,19\%\,,$ just multiply by
$\,1.19\,$:

Notice that when you *increase*,
you multiply by a number greater than $\,1\,.$

If you decrease *any* amount
by $\,30\%\,,$ then $\,70\%\,$ remains:

Thus, to decrease *any*
amount by $\,30\%\,,$
just multiply by $\,0.7\,.$
Notice that when you *decrease*,
you multiply by a number less than $\,1\,.$

Combining these ideas:

$\$50$ | original amount |

$(1.19)(\$50)$ | new amount, after the $\,19\%\,$ increase |

$(0.7)\cdot (1.19)(\$50)$ | new amount, after the $\,30\%\,$ decrease |

$(0.7)(1.19)(\$50) = \$41.65$ | round dollar amounts (as needed) to two decimal places |

What if we switch the order of applying the increase/decrease?

$\$50$ | original amount |

$(0.7)(\$50)$ | new amount, after the $\,30\%\,$ decrease |

$(1.19)\cdot (0.7)(\$50)$ | new amount, after the $\,19\%\,$ increase |

$(1.19)(0.7)(\$50) = \$41.65$ | round dollar amounts (as needed) to two decimal places |

Same result! Since $\,(1.19)(0.7) = (0.7)(1.19)\,,$ you can do the multiplication in whatever order you prefer.

In this exercise, all answers are rounded to two decimal places.

## Concept Practice

All answers are rounded to two decimal places.