Increase and Decrease an Amount by a Percent – Word Problems 2

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Question 1 of 4

1. Question
A shop retailer has an end of summer sale where a range of t-shirts are discounted by $32%$ . If these t-shirts normally cost $$18$ , what is the new price?
- $$$ (12.24)
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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 $32%$ of the original amount, $$18$ . Use fractions for easier computation.

$32%times$ $18$

$=$ $32/100times18/1$ Convert to fraction form

$=$ $576/100$ Simplify

$=$ $$5.76$ Move the decimal points $2$ places to the left

Next, use the formula to get the new amount

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

$=$ $18$ $-$ $5.76$

$=$ $$12.24$

The new price of the t-shirts with a $32%$ discount is $$12.24$

$$12.24$
Question 2 of 4

2. Question
A retailer has discounted a pair of running shoes by $45%$ . Find the new price if the normal price is $$110$ .
- $$$ (60.50, 60.5)
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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

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

First, solve for $45%$ of the original amount, $$110$ . Use decimals for easier computation.

$45%times$ $110$

$=$ $45/100times110$ Convert percentage to fraction

$=$ $0.45times110$ Convert fraction to decimal

$=$ $$49.50$

Next, use the formula to get the new amount

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

$=$ $110$ $-$ $49.50$

$=$ $$60.50$

The new price of the running shoes with a $32%$ discount is $$60.50$

$$60.50$

Question 3 of 4

A bag is on sale at a

$30%$ discount. If the original price is

$$52$ , what is the new selling price?

$$$ (36.40, 36.4)

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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

$30%$ of the original amount, $$52$ . Use decimals for easier computation.

	$30%times$ $52$

$=$	$0.3times52$	Convert percentage to decimal
$=$	$$15.60$

Next, use the formula to get the new amount

$\mathsf{\color{#007DDC}{new\;amount}}$	$=$	$\mathsf{\color{#00880A}{original}}-\mathsf{\color{#9a00c7}{decrease}}$
	$=$	$52$ $-$ $15.60$
	$=$	$$36.40$

The new price of the bag with a

$30%$ discount is $$36.40$

$$36.40$

Method Two

Find the percentage of the new amount by subtracting the discount,

$30%$ , from

$100%$

$100%-30%$

$=$

$70%$

Next, compute for $70%$ of the original price. Use decimals for easier computation.

$\mathsf{new\;amount}$	$=$	$\mathsf{percentage}\times\mathsf{original\;amount}$
	$=$	$70%$ $times52$
	$=$	$0.7times52$	Convert percentage to decimal
	$=$	$$36.40$

The new price of the bag with a

$30%$ discount is

$$36.40$

Question 4 of 4

Patrick bought a new off-road vehicle for $$36{,}000$ . After one year, it depreciates by

$12 1/2%$ . What is the new value of the vehicle?

$$$ (31500, 31,500)

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Transforming a Fraction from Mixed to Improper

$=$

$\frac{(\color{#9a00c7}{c}\times\color{#00880A}{a})+\color{#007DDC}{b}}{\color{#9a00c7}{c}}$

Decreasing Amount by Percentage

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

First, change the mixed number into an improper fraction by multiplying the denominator by the whole number and then add the numerator

$\color{#00880A}{12}\frac{\color{#007DDC}{1}}{\color{#9a00c7}{2}}$	$=$	$\frac{(\color{#00880A}{12}\times\color{#9a00c7}{2})+\color{#007DDC}{1}}{\color{#9a00c7}{2}}$

	$=$	$\frac{24+1}{2}$

	$=$	$\frac{25}{2}\%$

Then, convert the percentage to a fraction by having

$100$ as the percentage value’s denominator

Dividing fractions is the same as multiplying the dividend by the divisor’s reciprocal

$\text(Fraction)$	$=$	$\frac{\frac{25}{2}}{\color{#CC0000}{100}}$

	$=$	$\frac{25}{2}\div{\color{#CC0000}{100}}$	Change from a fraction to division

	$=$	$\frac{25}{2}\times\frac{1}{100}$	Get the divisor’s reciprocal then multiply

	$=$	$\frac{25}{200}$	Simplify

	$=$	$\frac{1}{8}$

Next, solve for

$1/8$ of the original amount, $$36{,}000$ .

	$\frac{1}{8}\times\color{00880A}{36{,}000}$

$=$	$\frac{1}{8}\times\frac{36{,}000}{1}$	Convert to fraction form

$=$	$\frac{36{,}000}{8}$	Simplify

Divide the values using long division

Since

$8$ cannot go into

$3$ , include

$6$ so that we have

$36$ instead. Write the answer above

Multiply

$4$ to

$8$ and write the product below

$36$

Subtract

$32$ from

$36$ and write the difference one line below

Bring down

$0$ so that

$4$ becomes

$40$

Divide

$40$ by

$8$ and write the answer after

$4$

Multiply

$4$ to

$8$ and write the product below

$40$

Since

$40-40$ is solved, the difference is

$0$ . So simply copy the two remaining zeroes.

This means $\frac{36{,}000}{8}=4500$

Next, use the formula to get the new amount

$\mathsf{\color{#007DDC}{new\;amount}}$	$=$	$\mathsf{\color{#00880A}{original}}-\mathsf{\color{#9a00c7}{decrease}}$
	$=$	$\color{00880A}{36{,}000}-\color{9a00c7}{4500}$
	$=$	$31{,}500$

The new value of the vehicle after it depreciates

$12 1/2%$ is $$31{,}500$

$$31{,}500$

Increase and Decrease an Amount by a Percent – Word Problems 2

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Quiz summary

Information

1. Question

Hint

Excellent!

Decreasing Amount by Percentage

2. Question

Hint

Great Work!

Decreasing Amount by Percentage

3. Question

Hint

Fantastic!

Decreasing Amount by Percentage

4. Question

Hint

Excellent!

Transforming a Fraction from Mixed to Improper

Decreasing Amount by Percentage

Quizzes

	$32%times$ $18$

$=$	$32/100times18/1$	Convert to fraction form

$=$	$576/100$	Simplify

$=$	$$5.76$	Move the decimal points $2$ places to the left

$\mathsf{\color{#007DDC}{new\;amount}}$	$=$	$\mathsf{\color{#00880A}{original}}-\mathsf{\color{#9a00c7}{decrease}}$
	$=$	$18$ $-$ $5.76$
	$=$	$$12.24$

	$45%times$ $110$

$=$	$45/100times110$	Convert percentage to fraction

$=$	$0.45times110$	Convert fraction to decimal
$=$	$$49.50$

$\mathsf{\color{#007DDC}{new\;amount}}$	$=$	$\mathsf{\color{#00880A}{original}}-\mathsf{\color{#9a00c7}{decrease}}$
	$=$	$110$ $-$ $49.50$
	$=$	$$60.50$