Find Original Amount Before Percent Change (Unitary Method)

Question 1 of 3

After a

20 %

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

$ 600

$$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.

New price = $ 600

$\text(New price)=$600$

Percentage of original price = 100 %

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

Percentage of new price = 100 + 20 = 120 %

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

Original price = ?

$\text(Original price)=?$

1 % Method - Unitary Method

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

For this method, find

1 %

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

$120 %$ $120%$	$=$ $=$	$$ 600$ $$600$

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

Hence,

1 %

$1%$ of the original amount is

$ 5

$$5$ .

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

1 %

$1%$ value, which is

5

$5$ , by

100

$100$ .

$100 %$ $100%$	$=$ $=$	$5 \times 100$ $5times100$
	$=$ $=$	$500$ $500$

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

$ 500

$$500$

Proportion Method

$\text(Proportion Method)$

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 $x$ $x$

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

$120 \times x$ $120timesx$	$=$ $=$	$600 \times 100$ $600times100$	Cross multiply
$120 x$ $120x$	$=$ $=$	$60{,}000$
$120 x$ $120x$ $\div 120$ $divide120$	$=$ $=$	$60{,}000\color{#CC0000}{\div120}$	Divide both sides by $120$ $120$

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

$x$ $x$	$=$ $=$	$500$ $500$

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

$ 500

$$500$

Question 2 of 3

A carpenter charges

$ 990

$$990$ for his work, which includes a

10 %

$10%$ 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.

Price with tax = $ 990

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

Percentage of price without tax = 100 %

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

Percentage of price with tax = 100 + 10 = 110 %

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

Price without tax = ?

$\text(Price without tax)=?$

1 % Method - Unitary Method

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

For this method, find

1 %

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

$110 %$ $110%$	$=$ $=$	$$ 990$ $$990$

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

Hence,

1 %

$1%$ of the original amount is

$ 9

$$9$ .

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

1 %

$1%$ value, which is

9

$9$ , by

100

$100$ .

$100 %$ $100%$	$=$ $=$	$9 \times 100$ $9times100$
	$=$ $=$	$900$ $900$

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

$ 900

$$900$

Proportion Method

$\text(Proportion Method)$

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 $x$ $x$

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

$110 \times x$ $110timesx$	$=$ $=$	$990 \times 100$ $990times100$	Cross multiply
$110 x$ $110x$	$=$ $=$	$99{,}000$
$110 x$ $110x$ $\div 110$ $divide110$	$=$ $=$	$99{,}000\color{#CC0000}{\div110}$	Divide both sides by $110$ $110$

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

$x$ $x$	$=$ $=$	$900$ $900$

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

$ 900

$$900$

Question 3 of 3

After a

12.5 %

$12.5%$ discount, a bed is now worth

$ 730

$$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.

New price = $ 730

$\text(New price)=$730$

Percentage of original price = 100 %

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

Percentage of new price = 100 - 12.5 = 87.5 %

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

Original price = ?

$\text(Original price)=?$

1 % Method - Unitary Method

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

For this method, find

1 %

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

$87.5 %$ $87.5%$	$=$ $=$	$$ 730$ $$730$

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

Hence,

1 %

$1%$ of the original amount is

$ 8.3429

$$8.3429$ .

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

1 %

$1%$ value, which is

8.3429

$8.3429$ , by

100

$100$ .

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

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

$ 834

$$834$

Proportion Method

$\text(Proportion Method)$

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 $x$ $x$

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

$87.5 \times x$ $87.5timesx$	$=$ $=$	$730 \times 100$ $730times100$	Cross multiply
$87.5 x$ $87.5x$	$=$ $=$	$73{,}000$
$87.5 x$ $87.5x$ $\div 87.5$ $divide87.5$	$=$ $=$	$73{,}000\color{#CC0000}{\div87.5}$	Divide both sides by $87.5$ $87.5$

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

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

$ 834

$$834$

Find Original Amount Before Percent Change (Unitary Method)

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