Find Original Amount Before Percent Change (Unitary Method)

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Question 1 of 3

After a

$20%$ price rise, a smartphone is now worth

$$600$ . What was its original price?

$$$ (500)

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First, use a rectangle and list down the values: percentages on the left side and amounts on the right side.

$\text(New price)=$600$

$\text(Percentage of original price)=100%$

$\text(Percentage of new price)=100+20=120%$

$\text(Original price)=?$

$1% \text(Method) -\text(Unitary Method)$

For this method, find

$1%$ of the original amount by dividing both known values by $120$ .

$120%$	$=$	$$600$

$120$ $divide120$	$=$	$600$ $divide120$	Divide both sides by $120$
$1$	$=$	$5$

Hence,

$1%$ of the original amount is

$$5$ .

To find the original price, which is $100%$ of the value, multiply the

$1%$ value, which is

$5$ , by

$100$ .

$100%$	$=$	$5times100$
	$=$	$500$

Hence, the original price of the smartphone was $\underline{\color{#9a00c7}{$500}}$

$$500$

$\text(Proportion Method)$

To find the missing value, cross-multiply the fraction of the percentages by the fraction of the given and total value.

Let the original price be $x$

$\frac{\color{#007DDC}{120}}{\color{#e85e00}{100}}$	$=$	$\frac{\color{#00880A}{600}}{\color{#9a00c7}{x}}$

$120timesx$	$=$	$600times100$	Cross multiply
$120x$	$=$	$60{,}000$
$120x$ $divide120$	$=$	$60{,}000\color{#CC0000}{\div120}$	Divide both sides by $120$

$x$	$=$	$\frac{6000}{12}$	Simplify

$x$	$=$	$500$

Hence, the original price of the smartphone was $\underline{\color{#9a00c7}{$500}}$

$$500$

Question 2 of 3

A carpenter charges

$$990$ for his work, which includes a

$10%$ tax. How much does the carpenter originally charge?

$$$ (900)

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First, use a rectangle and list down the values: percentages on the left side and amounts on the right side.

$\text(Price with tax)=$990$

$\text(Percentage of price without tax)=100%$

$\text(Percentage of price with tax)=100+10=110%$

$\text(Price without tax)=?$

$1% \text(Method) -\text(Unitary Method)$

For this method, find

$1%$ of the original amount by dividing both known values by $110$ .

$110%$	$=$	$$990$

$110$ $divide110$	$=$	$990$ $divide110$	Divide both sides by $110$
$1$	$=$	$9$

Hence,

$1%$ of the original amount is

$$9$ .

To find the original price, which is $100%$ of the value, multiply the

$1%$ value, which is

$9$ , by

$100$ .

$100%$	$=$	$9times100$
	$=$	$900$

Hence, the original charge is $\underline{\color{#9a00c7}{$900}}$

$$900$

$\text(Proportion Method)$

To find the missing value, cross-multiply the fraction of the percentages by the fraction of the given and total value.

Let the original price be $x$

$\frac{\color{#007DDC}{110}}{\color{#e85e00}{100}}$	$=$	$\frac{\color{#00880A}{990}}{\color{#9a00c7}{x}}$

$110timesx$	$=$	$990times100$	Cross multiply
$110x$	$=$	$99{,}000$
$110x$ $divide110$	$=$	$99{,}000\color{#CC0000}{\div110}$	Divide both sides by $110$

$x$	$=$	$\frac{9900}{11}$	Simplify

$x$	$=$	$900$

Hence, the original charge is $\underline{\color{#9a00c7}{$900}}$

$$900$

Question 3 of 3

After a

$12.5%$ discount, a bed is now worth

$$730$ . What was its original price?

Round to the nearest dollar amount

$$$ (834)

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First, use a rectangle and list down the values: percentages on the left side and amounts on the right side.

$\text(New price)=$730$

$\text(Percentage of original price)=100%$

$\text(Percentage of new price)=100-12.5=87.5%$

$\text(Original price)=?$

$1% \text(Method) -\text(Unitary Method)$

For this method, find

$1%$ of the original amount by dividing both known values by $87.5$ .

$87.5%$	$=$	$$730$

$87.5$ $divide87.5$	$=$	$730$ $divide87.5$	Divide both sides by $87.5$
$1$	$=$	$8.3429$	Rounded to four decimal places

Hence,

$1%$ of the original amount is

$$8.3429$ .

To find the original amount, which is $100%$ of the value, multiply the

$1%$ value, which is

$8.3429$ , by

$100$ .

$100%$	$=$	$8.3429times100$
	$=$	$834.29$
	$=$	$834$	Round to the nearest whole number

Hence, the original price of the bed was $\underline{\color{#9a00c7}{$834}}$

$$834$

$\text(Proportion Method)$

To find the missing value, cross-multiply the fraction of the percentages by the fraction of the given and total value.

Let the original price be $x$

$\frac{\color{#007DDC}{87.5}}{\color{#e85e00}{100}}$	$=$	$\frac{\color{#00880A}{730}}{\color{#9a00c7}{x}}$

$87.5timesx$	$=$	$730times100$	Cross multiply
$87.5x$	$=$	$73{,}000$
$87.5x$ $divide87.5$	$=$	$73{,}000\color{#CC0000}{\div87.5}$	Divide both sides by $87.5$

$x$	$=$	$834.28571$
$x$	$=$	$834$	Round to the nearest whole number

Hence, the original price of the bed was $\underline{\color{#9a00c7}{$834}}$

$$834$

Find Original Amount Before Percent Change (Unitary Method)

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