Question

A shirt is on sale for 60% off. If the sale price is $16, what was the original price?

Answer 1

$40

Explanation:

We can represent the price of an item on sale for
`x\%` off as:

`S=P \cdot (100-x)/(100)`,

where P is the product's original price and S is the sale price.

Applying this to the problem at hand:

`\$16=P \cdot (100-60)/(100)`

↓ simplifying the fraction

`\$16=P \cdot (2)/(5)`

To solve for P in this equation (the original price), we have to multiply both sides of the equation by the reciprocal of its coefficient.

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Remember that any fraction multiplied by its reciprocal is 1:

`(2)/(5) \cdot (5)/(2) = (10)/(10) = 1`

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`(5)/(2) \left( \$16\right)= \left(P \cdot (2)/(5)\right)(5)/(2)`

`\boxed{\$40 = P}`

So, the original price of the shirt was $40.