Question

Joyce paid $48.00 for an item at the store that was 40 percent off the original price. What was the original price?

$


Give your answer to the nearest cent.

Answer 1

`\Huge \boxed{\boxed{\bf{\$80.00}}}`

Step-by-step explanation:

A 40% reduction means that the item cost 60% of the original price.

Method 1

You can use the unitary method to find 1% of the original price:

➽
`\tt{60\%\,\ of\;\ the\,\ original\,\ price = \$48}`

• 
  `\tt{1\%\,\ of\,\ the\,\ original\,\ price = 48\,\ /\,\ 60 }`

• 
  `\tt{1\%\,\ of\,\ the\,\ original\,\ price = \$0.80}`

➽
`\tt{100\%\,\ of\,\ the\,\ original\,\ price = 0.80 * 100}`

• 
  `\tt{100\%\,\ of\,\ the\,\ original\,\ price = \$80}`

Method 2

Another way to do this is the inverse operation:

To work out 60% of the price, you multiply by 0.6.

`\boxed{\tt{Original \,\ Price \longrightarrow Sale \,\ Price}}`

• 
  `\tt{Original \,\ Price * 0.6 = Sale \,\ Price`

The inverse (opposite) of multiplying by 0.6 is dividing by 0.6.

`\boxed{\tt{\$??? \longleftarrow Sale\,\ Price}}`

• 
  `\tt{Sale\,\ Price\ / \$???}`

To calculate the original price, we divide the sale price by 0.6.

`\begin{aligned}\tt{\texttt{Original Price} &= \texttt{Sale Price} / 0.60} \\\tt{&= \$48 / 0.60} \\\tt{&= \$80}\end{aligned}`

Therefore, the original price was $80.00.

#BTH1

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