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Find Original Amount Before Percent Change (Proportions)>
Find Original Amount Before Percent Change (Unitary Method)Find Original Amount Before Percent Change (Unitary Method)
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Question 1 of 3
1. Question
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, crossmultiply 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
2. Question
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, crossmultiply 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
3. Question
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)=10012.5=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, crossmultiply 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`
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