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Increase and Decrease an Amount by a Percent: Word Problems>
Increase and Decrease an Amount by a Percent – Word Problems 1Increase and Decrease an Amount by a Percent – Word Problems 1
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Question 1 of 4
1. Question
A pair of `$200` runners are reduced by `18%`. What is the new selling price?- `$` (164)
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Well Done!
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A percentage describes an amount’s relation to a whole. Dividing it by `100` converts it into a fraction.Decreasing Amount by Percentage
$$\mathsf{\color{#007DDC}{new\;amount}}=\mathsf{\color{#00880A}{original}}-\mathsf{\color{#9a00c7}{decrease}}$$First, solve for `18%` of the original amount, `$200`. Use fractions for easier computation.`18%times``200` `=` `18/100times200/1` Convert to fraction form `=` `18/1times2/1` Simplify `=` $$\frac{36}{1}$$ `=` `$36` Next, use the formula to get the new amount$$\mathsf{\color{#007DDC}{new\;amount}}$$ `=` $$\mathsf{\color{#00880A}{original}}-\mathsf{\color{#9a00c7}{decrease}}$$ `=` `200``-``36` `=` `$164` The new price of the pair of runners with an `18%` discount is `$164``$164` -
Question 2 of 4
2. Question
An online technology store advertises a `33 1/3 %` discount on a bluetooth speaker. If the original cost is `$390`, what is the new selling price?- `$` (260)
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Excellent!
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A percentage describes an amount’s relation to a whole. Dividing it by `100` converts it into a fraction.Decreasing Amount by Percentage
$$\mathsf{\color{#007DDC}{new\;amount}}=\mathsf{\color{#00880A}{original}}-\mathsf{\color{#9a00c7}{decrease}}$$First, solve for `33 1/3%` of the original amount, `$390`. Use fractions for easier computation.`33 1/3%times``390` `=` `1/3times390/1` Convert to fraction form `=` $$\frac{390}{3}$$ `=` `$130` Next, use the formula to get the new amount$$\mathsf{\color{#007DDC}{new\;amount}}$$ `=` $$\mathsf{\color{#00880A}{original}}-\mathsf{\color{#9a00c7}{decrease}}$$ `=` `390``-``130` `=` `$260` The new price of the speaker with a `33 1/3%` discount is `$260``$260` -
Question 3 of 4
3. Question
A motorcycle costs `$3700` but has been discounted by `30%`. What is the new selling price?- `$` (2590)
Hint
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Exceptional!
Incorrect
A percentage describes an amount’s relation to a whole. Dividing it by `100` converts it into a fraction.Decreasing Amount by Percentage
$$\mathsf{\color{#007DDC}{new\;amount}}=\mathsf{\color{#00880A}{original}}-\mathsf{\color{#9a00c7}{decrease}}$$First, solve for `30%` of the original amount, `$3700`. Use fractions for easier computation.`30%times``3700` `=` `30/100times3700/1` Convert to fraction form `=` `30/1times37/1` `=` $$\frac{1110}{1}$$ `=` `$1110` Next, use the formula to get the new amount$$\mathsf{\color{#007DDC}{new\;amount}}$$ `=` $$\mathsf{\color{#00880A}{original}}-\mathsf{\color{#9a00c7}{decrease}}$$ `=` `3700``-``1110` `=` `$2590` The new price of the motorcycle with a `30%` discount is `$2590``$2590` -
Question 4 of 4
4. Question
Last year, the price of a luxury car was $$$61{,}750$$. If there is a `9.5%` increase on its price this year, what will the luxury car’s new price be?- `$` (67616.25)
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Nice Job!
Incorrect
A percentage describes an amount’s relation to a whole. Moving the value’s decimal point `2` places to the left converts it into a decimal.Increasing Amount by Percentage
$$\mathsf{\color{#007DDC}{new\;amount}}=\mathsf{\color{#00880A}{original}}+\mathsf{\color{#9a00c7}{increase}}$$Method OneFirst, solve for `9.5%` of the original amount, $$$61{,}750$$. Use decimals for easier computation.$$9.5\%\times\color{00880A}{61{,}750}$$ `=` $$\frac{9.5}{100}\times\frac{61{,}750}{1}$$ Convert to fraction form `=` $$\frac{586{,}625}{100}$$ `=` `$5866.25` Move the decimal point two places to the left Next, use the formula to get the new amount$$\mathsf{\color{#007DDC}{new\;amount}}$$ `=` $$\mathsf{\color{#00880A}{original}}+\mathsf{\color{#9a00c7}{increase}}$$ `=` $$\color{00880A}{61{,}750}+\color{9a00c7}{5866.25}$$ `=` $$67{,}616.25$$ The new price of the luxury car with a `9.5%` price increase is $$$67{,}616.25$$$$$67{,}616.25$$Method TwoFind the percentage of the new amount by adding the sales tax, `9.5%`, to `100%``100%+9.5%` `=` `109.5%` Next, compute for `109.5%` of the original price. Use decimals for easier computation.$$\color{A57200}{109.5\%}\times61{,}750$$ `=` $$\frac{109.5}{100}\times61{,}750$$ Convert percentage to fraction `=` $$1.095\times61{,}750$$ Convert fraction to decimal `=` $$67{,}616.25$$ The new price of the luxury car with a `9.5%` price increase is $$$67{,}616.25$$$$$67{,}616.25$$
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