Math CentralQuandaries & Queries


Question from Saira:

If the sale price is $\$55.50$ and the discount is 12% what is the regular price?

Hi Saira,

I think of this as viewing a process from the end, looking back at the beginning, the beginning being the starting price and the end the sale price. If you knew the starting price you could go forward, by that I mean

the regular price minus 12% of the starting price is the sale price.

Let's say that algebraically. Let the regular price be $x$ dollars and since $12\% = \frac{12}{100} = 0.12$ then the "forward equation" is

\[x - 0.12 \times x = 55.50 \mbox{ dollars.}\]

This simplifies to

\[(1 - 0.12)x = 55.50\]


\[0.88 x = 55.50.\]

Solve for $x.$


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