Percent of Change – Word Problems

Question 1 of 6

A shop retailer increased the price of his best-selling sunglasses from

$ 24

$$24$ to

$ 30

$$30$ . Find the percentage change.

(25) $%$ $%$

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Percent Change Between Two Amounts

$\mathsf{\frac{\color{#9a00c7}{change}}{\color{#00880A}{original}}}=\frac{r}{100}$

Amount of Change

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

First, compute for the amount of change

$\mathsf{\color{#9a00c7}{change}}$	$=$	$\mathsf{\color{#007DDC}{new\;amount}}-\mathsf{\color{#00880A}{original}}$
	$=$	$\color{#007DDC}{30}-\color{#00880A}{24}$
	$=$	$$6$

Use the formula to get the value of percent change $(r)$

$\mathsf{\frac{\color{#9a00c7}{change}}{\color{#00880A}{original}}}$	$=$	$\frac{r}{100}$

$\frac{\color{#9a00c7}{6}}{\color{#00880A}{24}}$	$=$	$\frac{r}{100}$

$24r$	$=$	$6(100)$	Cross multiply
$24r$	$=$	$600$

$r$	$=$	$\frac{600}{24}$

$r$	$=$	$25%$

$25%$

Question 2 of 6

A painting bought last year for

$$800$ just sold this year for

$$1200$ . What is the percentage profit?

(50) $%$

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Percent Profit Between Two Amounts

$\mathsf{percent\;profit}=\mathsf{\frac{\color{#9a00c7}{profit}}{\color{#00880A}{original}}}\times\frac{100}{1}$

Amount of Profit

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

First, compute for the amount of profit

$\mathsf{\color{#9a00c7}{profit}}$	$=$	$\mathsf{\color{#007DDC}{new\;price}}-\mathsf{\color{#00880A}{original}}$
	$=$	$\color{#007DDC}{1200}-\color{#00880A}{800}$
	$=$	$$400$

Use the formula to get the percent profit.

$\mathsf{percent\;profit}$	$=$	$\mathsf{\frac{\color{#9a00c7}{profit}}{\color{#00880A}{original}}}\times\frac{100}{1}$

	$=$	$\frac{\color{#9a00c7}{400}}{\color{#00880A}{800}}\times\frac{100}{1}$

	$=$	$\frac{4}{8}\times\frac{100}{1}$	Cancel the zeroes

	$=$	$\frac{400}{8}$

	$=$	$50\%$

$50%$

Question 3 of 6

A t-shirt originally costs

$$20$ . Later, it sells for

$$24$ . What is the percentage profit?

(20) $%$

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Percent Profit Between Two Amounts

$\mathsf{percent\;profit}=\mathsf{\frac{\color{#9a00c7}{profit}}{\color{#00880A}{original}}}\times\frac{100}{1}$

Amount of Profit

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

First, compute for the amount of profit

$\mathsf{\color{#9a00c7}{profit}}$	$=$	$\mathsf{\color{#007DDC}{new\;price}}-\mathsf{\color{#00880A}{original}}$
	$=$	$\color{#007DDC}{24}-\color{#00880A}{20}$
	$=$	$$4$

Use the formula to get the percent profit.

$\mathsf{percent\;profit}$	$=$	$\mathsf{\frac{\color{#9a00c7}{profit}}{\color{#00880A}{original}}}\times\frac{100}{1}$

	$=$	$\frac{\color{#9a00c7}{4}}{\color{#00880A}{20}}\times\frac{100}{1}$

	$=$	$\frac{400}{20}$

	$=$	$\frac{40}{2}$	Cancel the zeroes

	$=$	$20\%$

$20%$

Question 4 of 6

A car dealer purchases a vehicle wholesale for a cost of $$19{,}500$ . Later, he sells it for $$26{,}300$ . What is the percentage profit?

Round off answer to

$1$ decimal place.

(34.9) $%$

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Percent Profit Between Two Amounts

$\mathsf{percent\;profit}=\mathsf{\frac{\color{#9a00c7}{profit}}{\color{#00880A}{original}}}\times\frac{100}{1}$

Amount of Profit

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

First, compute for the amount of profit

$\mathsf{\color{#9a00c7}{profit}}$	$=$	$\mathsf{\color{#007DDC}{new\;price}}-\mathsf{\color{#00880A}{original}}$
	$=$	$\color{#007DDC}{26{,}300}-\color{#00880A}{19{,}500}$
	$=$	$$6800$

Use the formula to get the percent profit.

$\mathsf{percent\;profit}$	$=$	$\mathsf{\frac{\color{#9a00c7}{profit}}{\color{#00880A}{original}}}\times\frac{100}{1}$

	$=$	$\frac{\color{#9a00c7}{6800}}{\color{#00880A}{19{,}500}}\times\frac{100}{1}$

	$=$	$\frac{6800}{195}$	Cancel the zeroes

	$=$	$34.9\%$

$34.9%$

Question 5 of 6

A

$90$ -gram snack bar is now

$18$ grams heavier. What is the percent increase on its weight?

(20) $%$

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Percent Increase Between Two Amounts

$\mathsf{percent\;increase}=\mathsf{\frac{\color{#9a00c7}{increase}}{\color{#00880A}{original}}}\times\frac{100}{1}$

Amount of Increase

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

Use the formula to get the percent increase

$\mathsf{percent\;increase}$	$=$	$\mathsf{\frac{\color{#9a00c7}{increase}}{\color{#00880A}{original}}}\times\frac{100}{1}$

	$=$	$\frac{\color{#9a00c7}{18}}{\color{#00880A}{90}}\times\frac{100}{1}$

	$=$	$\frac{18}{9}\times\frac{10}{1}$	Cancel the zeroes

	$=$	$\frac{18\times10}{9\times1}$

	$=$	$\frac{180}{9}$

	$=$	$20%$

$20%$

Question 6 of 6

A snack bar used to contain

$12$ g of sugar. Now it contains

$3$ g less sugar. What is the percentage decrease in sugar?

(25) $%$

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Percent Decrease Between Two Amounts

$\mathsf{percent\;decrease}=\mathsf{\frac{\color{#9a00c7}{decrease}}{\color{#00880A}{original}}}\times\frac{100}{1}$

Use the formula to get the percent decrease

$\mathsf{percent\;decrease}$	$=$	$\mathsf{\frac{\color{#9a00c7}{decrease}}{\color{#00880A}{original}}}\times\frac{100}{1}$

	$=$	$\frac{\color{#9a00c7}{3}}{\color{#00880A}{12}}\times\frac{100}{1}$

	$=$	$\frac{1}{4}\times\frac{100}{1}$	Cancel the zeroes

	$=$	$\frac{25}{1}$

	$=$	$25%$

$25%$

Percent of Change – Word Problems

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Quiz summary

Information

1. Question

Hint

Well Done!

Percent Change Between Two Amounts

Amount of Change

2. Question

Hint

Great Work!

Percent Profit Between Two Amounts

Amount of Profit

3. Question

Hint

Excellent!

Percent Profit Between Two Amounts

Amount of Profit

4. Question

Hint

Well Done!

Percent Profit Between Two Amounts

Amount of Profit

5. Question

Hint

Fantastic!

Percent Increase Between Two Amounts

Amount of Increase

6. Question

Hint

Exceptional!

Percent Decrease Between Two Amounts

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