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Find Base from Percent of an Amount (Unitary Method)>
Find Base from Percent of an Amount (Unitary Method) 2Find Base from Percent of an Amount (Unitary Method) 2
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Question 1 of 4
1. Question
`2%` of an amount is `$70`. Find the original amount.- `$` (3500)
Hint
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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(Known value)=$70``\text(Percentage of known value)=2%``\text(Percentage of total value)=100%``\text(Total value)=?`
`\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 amount be `x`$$\frac{\color{#007DDC}{2}}{\color{#e85e00}{100}}$$ `=` $$\frac{\color{#00880A}{70}}{\color{#9a00c7}{x}}$$ `2timesx` `=` `70times100` Cross multiply `2x` `=` $$7000$$ `2x``divide2` `=` $$7000\color{#CC0000}{\div2}$$ Divide both sides by `2` `x` `=` `3500` Hence, `$70` is `2%` of $$\underline{\color{#9a00c7}{$3500}}$$`$3500``1% \text(Method) -\text(Unitary Method)`First, find the `1%` of the total value by dividing both known values by `2`.`2%` `=` `$70` `2``divide2` `=` `70``divide2` Divide both sides by `2` `1` `=` `35` Hence, `1%` of the original amount is `$35`.To find the total value, which is `100%` of the value, multiply the `1%` value, which is `35`, by `100`.`100%` `=` `35times100` `=` `3500` Hence, `$70` is `2%` of $$\underline{\color{#9a00c7}{$3500}}$$`$3500` -
Question 2 of 4
2. Question
`8%` of an amount is `$72`. Find the original amount.- `$` (900)
Hint
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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(Known value)=$72``\text(Percentage of known value)=8%``\text(Percentage of total value)=100%``\text(Total value)=?`
`\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 amount be `x`$$\frac{\color{#007DDC}{8}}{\color{#e85e00}{100}}$$ `=` $$\frac{\color{#00880A}{72}}{\color{#9a00c7}{x}}$$ `8timesx` `=` `72times100` Cross multiply `8x` `=` $$7200$$ `8x``divide8` `=` $$7200\color{#CC0000}{\div8}$$ Divide both sides by `8` `x` `=` `900` Hence, `$72` is `8%` of $$\underline{\color{#9a00c7}{$900}}$$`$900``1% \text(Method) -\text(Unitary Method)`First, find the `1%` of the total value by dividing both known values by `8`.`8%` `=` `$72` `8``divide8` `=` `72``divide8` Divide both sides by `8` `1` `=` `9` Hence, `1%` of the original amount is `$9`.To find the total value, which is `100%` of the value, multiply the `1%` value, which is `9`, by `100`.`100%` `=` `9times100` `=` `900` Hence, `$72` is `8%` of $$\underline{\color{#9a00c7}{$900}}$$`$900` -
Question 3 of 4
3. Question
`42%` of an amount is `77 \text(cm)`. Find the original amount.Round your answer to one decimal place- (183.3) `\text(cm)`
Hint
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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(Known value)=77 \text(cm)``\text(Percentage of known value)=42%``\text(Percentage of total value)=100%``\text(Total value)=?`
`\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 amount be `x`$$\frac{\color{#007DDC}{42}}{\color{#e85e00}{100}}$$ `=` $$\frac{\color{#00880A}{77}}{\color{#9a00c7}{x}}$$ `42timesx` `=` `77times100` Cross multiply `42x` `=` $$7700$$ `42x``divide42` `=` $$7700\color{#CC0000}{\div42}$$ Divide both sides by `42` `x` `=` `183.3` Rounded to one decimal place Hence, `77 \text(cm)` is `42%` of $$\underline{\color{#9a00c7}{183.3\;\text{cm}}}$$`183.3 \text(cm)``1% \text(Method) -\text(Unitary Method)`First, find the `1%` of the total value by dividing both known values by `42`.`42%` `=` `77 \text(cm)` `42``divide42` `=` `77``divide42` Divide both sides by `42` `1` `=` `1.833…` Hence, `1%` of the original amount is `1.833… \text(cm)`.To find the total value, which is `100%` of the value, multiply the `1%` value, which is `1.833…`, by `100`.`100%` `=` `1.833…times100` `=` `183.3` Rounded to one decimal place Hence, `77 \text(cm)` is `42%` of $$\underline{\color{#9a00c7}{183.3\;\text{cm}}}$$`183.3 \text(cm)` -
Question 4 of 4
4. Question
Andrew earned `$481` as a commission for selling office furniture. If his commission rate is `9 1/4%` how much was made in sales?- `$` (5200)
Hint
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A commission is expressed as a percentage of the value of goods sold.First, summarise the data and draw a diagram for easier understanding of the problem`\text(Commission earned)=$481``\text(Commission rate)=9 1/4%``\text(Percentage of total sales)=100%``\text(Total sales)=?`
To find the missing value, cross-multiply the fraction of the percentages by the fraction of the given and total value.Let the original amount be `x`$$\frac{\color{#007DDC}{9\;\frac{1}{4}}}{\color{#e85e00}{100}}$$ `=` $$\frac{\color{#00880A}{481}}{\color{#9a00c7}{x}}$$ `9 1/4timesx` `=` `481times100` Cross multiply `9 1/4x` `=` $$48{,}100$$ `9 1/4x``divide9 1/4` `=` $$48{,}100\color{#CC0000}{\div9\;\frac{1}{4}}$$ Divide both sides by `9 1/4` `x` `=` `5200` Hence, Andrew’s total sales were $$\underline{\color{#9a00c7}{$5200}}$$`$5200`
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