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Increase and Decrease an Amount by a Percent: Word Problems>
Increase and Decrease an Amount by a Percent – Word Problems 2Increase 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
3. Question
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 OneFirst, 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 TwoFind 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``$36.40` -
Question 4 of 4
4. Question
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 denominatorDividing 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 $$$31{,}500$$$$$31{,}500$$
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