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Percent of Change – Word ProblemsPercent of Change – Word Problems
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Question 1 of 6
1. Question
A shop retailer increased the price of his best-selling sunglasses from `$24` to `$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
2. Question
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
3. Question
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
4. Question
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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Incorrect
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
5. Question
A `90`-gram snack bar is now `18` grams heavier. What is the percent increase on its weight?- (20)`%`
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Fantastic!
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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
6. Question
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)`%`
Hint
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Exceptional!
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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%`
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