Increase and Decrease an Amount by a Percent – Word Problems 3

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Question 1 of 3

1. Question
A jacket is $25%$ off its normal price which is $$189.95$ . What is the new selling price?

Round your answer to two decimal places
- $$$ (142.46)
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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.

Decreasing Amount by Percentage

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

Method One

First, solve for $25%$ of the original amount, $$189.95$ . Use decimals for easier computation.

$25%times$ $189.95$

$=$ $0.25times189.95$ Convert percentage to decimal

$=$ $$47.49$

Next, use the formula to get the new amount

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

$=$ $189.95$ $-$ $47.49$

$=$ $$142.46$

The new price of the jacket with a $25%$ discount is $$142.46$

$$142.46$

Method Two

Find the percentage of the new amount by subtracting the discount, $25%$ , from $100%$

$100%-25%$ $=$ $75%$

Next, compute for $75%$ of the original price. Use decimals for easier computation.

$75%$ $times189.95$

$=$ $0.75times189.95$ Convert percentage to decimal

$=$ $$142.46$

The new price of the jacket with a $25%$ discount is $$142.46$

$$142.46$

Question 2 of 3

A remote control aircraft costs

$$450$ . If a sales tax of

$7.25%$ is added, what is the new price?

Round your answer to two decimal places

$$$ (482.63)

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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

$7.25%$ of the original amount, $$450$ . Use fractions for easier computation.

	$7.25%times$ $450$

$=$	$7.25/100 times 450/1$	Convert to fraction form

$=$	$3262.5/100$

$=$	$32.625$	Move the decimal point two places to the left
$=$	$$32.63$	Round off to two decimal places

Next, use the formula to get the new amount

$\mathsf{\color{#007DDC}{new\;amount}}$	$=$	$\mathsf{\color{#00880A}{original}}+\mathsf{\color{#9a00c7}{increase}}$
	$=$	$450$ $+$ $32.63$
	$=$	$$482.63$

The new price of the remote control aircraft with a

$7.25%$ sales tax is $$482.63$

$$482.63$

Method Two

Find the percentage of the new amount by adding the sales tax,

$7.25%$ , to

$100%$

$100%+7.25%$

$=$

$107.25%$

Next, compute for $107.25%$ of the original price. Use decimals for easier computation.

	$107.25%$ $times450$

$=$	$107.25/100 times 450$	Convert percentage to fraction

$=$	$1.0725times450$	Convert fraction to decimal
$=$	$$482.63$

The new price of the remote control aircraft with a

$7.25%$ sales tax is

$$482.63$

Question 3 of 3

A hat costs

$$19.95$ . If a sales tax of

$6.75%$ is added, what is the new price?

Round your answer to two decimal places

$$$ (21.30, 21.3)

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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

$6.75%$ of the original amount, $$19.95$ . Use decimals for easier computation.

	$6.75%times$ $19.95$

$=$	$6.75/100times19.95/1$	Convert values to fractions

$=$	$0.0675times19.95$	Convert fraction to decimal

$=$	$1.346625$

$=$	$$1.35$	Round off to two decimal places

Next, use the formula to get the new amount

$\mathsf{\color{#007DDC}{new\;amount}}$	$=$	$\mathsf{\color{#00880A}{original}}+\mathsf{\color{#9a00c7}{increase}}$
	$=$	$19.95$ $+$ $1.35$
	$=$	$$21.30$

The new price of the hat with a

$6.75%$ sales tax is $$21.30$

$$21.30$

Method Two

Find the percentage of the new amount by adding the sales tax,

$7.25%$ , to

$100%$

$100%+6.75%$

$=$

$106.75%$

Next, compute for $106.75%$ of the original price. Use decimals for easier computation.

	$106.75%$ $times19.95$

$=$	$106.75/100times19.95$	Convert percentage to fraction

$=$	$1.0675times19.95$	Convert fraction to decimal
$=$	$$21.30$

The new price of the hat with a

$6.75%$ sales tax is $$21.30$

$$21.30$

Increase and Decrease an Amount by a Percent – Word Problems 3

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Quiz summary

Information

1. Question

Hint

Well Done!

Decreasing Amount by Percentage

2. Question

Hint

Good Job!

Increasing Amount by Percentage

3. Question

Hint

Excellent!

Increasing Amount by Percentage

Quizzes

	$25%times$ $189.95$

$=$	$0.25times189.95$	Convert percentage to decimal
$=$	$$47.49$

$\mathsf{\color{#007DDC}{new\;amount}}$	$=$	$\mathsf{\color{#00880A}{original}}-\mathsf{\color{#9a00c7}{decrease}}$
	$=$	$189.95$ $-$ $47.49$
	$=$	$$142.46$

	$75%$ $times189.95$
$=$	$0.75times189.95$	Convert percentage to decimal
$=$	$$142.46$