Math CentralQuandaries & Queries


Question from Dylan, a student:

shirts on sale for 25% off, the sale price is 12.75. What is the original price?

Hi Dylan,

With just a little algebra you can solve this.

Suppose the original price is $P$ dollars and the sale price is $S$ dollars. The discount is 25% so if you knew the original price then you would calculate the sale price using

\[P - 0.25 P = S.\]

Taking out a common factor of $P$ on the left side gives

\[P(1 - 0.25) = 0.75 P = S.\]

But you know $S,$ so solve for $P.$


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