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Problem 219

Geometry Difficulty 1.6 Multiple choice CEMC Gauss (Grade 8) · Canada · 2013

$PQRS$ is a rectangle with diagonals $PR$ and $QS$ , as shown.

The value of $y$ is

Pick one

Official solution

For every 3 chocolates that Claire buys at the regular price, she buys a fourth for 25 cents.

Consider dividing the 12 chocolates that Claire buys into 3 groups of 4 chocolates.

In each group of 4, Claire buys 3 chocolates at the regular price and the fourth chocolate is purchased for 25 cents.

That is, of the 12 chocolates that Claire buys, 3 are bought at 25 cents each while the remaining 9 are purchased at the regular price.

The total cost to purchase 3 chocolates at 25 cents each is $3\times25=75$ cents.

Since Claire spent 6.15 and the total cost of the 25 cent chocolates was 75 cents, then the cost of the regular price chocolates was \$6.15-\$0.75=\$5.40$.
Since 9 chocolates were purchased at the regular price for a total of 5.40, then the regular price of one chocolate is $\frac{\$5.40}{9}=\$0.60\$$ or 60 cents.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.