6.RP Shirt Sale
Selina bought a shirt on sale that was 20% less than the original price. The original price was \($ \)5 more than the sale price. What was the original price? Explain or show work.
Solutions
Solution: A tape diagram (known in some circles as a strip or bar diagram) shows the solution in a very succinct way:
Since the difference between the original price and the sale price is \($ \)5, which is also 20% of the original price, the original price is 5 times \($ \)5.
The original price was \($ \)25.
We know that 20% of the original price is \($ \)5. Furthermore, 20% of the original price is the same thing as \(\frac{20}{100}=\frac15\) of the original price. We know that \(\frac15\) of a quantity is 5, so we can solve this problem by dividing 5 by \(\frac15\) (this is a Group Size Unknown problem).
$$5 \div \frac15 = 25$$
So the original price was \($ \)25.
Commentary
There are several different ways to reason through this problem; two approaches are shown.