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)

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

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)

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

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 $x$ $x$

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

$110timesx$	$=$	$990times100$	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)

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

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)

Try VividMath Premium to unlock full access

Quiz summary

Information

1. Question

Hint

Great Work!

2. Question

Hint

Correct!

3. Question

Hint

Excellent!

Quizzes