Increase and Decrease an Amount by a Percent – Word Problems 1

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Question 1 of 4

1. Question
A pair of $$ 200$ $$200$ runners are reduced by $18 %$ $18%$ . What is the new selling price?
- $$$ $$$ (164)
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A percentage describes an amount’s relation to a whole. Dividing it by $100$ $100$ 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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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)
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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 $30%$ 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

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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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 One

First, 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 Two

Find 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$

Increase and Decrease an Amount by a Percent – Word Problems 1

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Quiz summary

Information

1. Question

Hint

Well Done!

Decreasing Amount by Percentage

2. Question

Hint

Excellent!

Decreasing Amount by Percentage

3. Question

Hint

Exceptional!

Decreasing Amount by Percentage

4. Question

Hint

Nice Job!

Increasing Amount by Percentage

Quizzes

	$18%times$ $200$

$=$	$18/100times200/1$	Convert to fraction form

$=$	$18/1times2/1$	Simplify

$=$	$\frac{36}{1}$

$=$	$$36$

$\mathsf{\color{#007DDC}{new\;amount}}$	$=$	$\mathsf{\color{#00880A}{original}}-\mathsf{\color{#9a00c7}{decrease}}$
	$=$	$200$ $-$ $36$
	$=$	$$164$

	$33 1/3%times$ $390$

$=$	$1/3times390/1$	Convert to fraction form

$=$	$\frac{390}{3}$

$=$	$$130$

$\mathsf{\color{#007DDC}{new\;amount}}$	$=$	$\mathsf{\color{#00880A}{original}}-\mathsf{\color{#9a00c7}{decrease}}$
	$=$	$390$ $-$ $130$
	$=$	$$260$

	$30%times$ $3700$

$=$	$30/100times3700/1$	Convert to fraction form

$=$	$30/1times37/1$

$=$	$\frac{1110}{1}$

$=$	$$1110$

$\mathsf{\color{#007DDC}{new\;amount}}$	$=$	$\mathsf{\color{#00880A}{original}}-\mathsf{\color{#9a00c7}{decrease}}$
	$=$	$3700$ $-$ $1110$
	$=$	$$2590$