Maths Olympiad Prep

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, 2013

Geometry Difficulty 1.6 Junior Find the answer Canada

PQRSPQRS is a rectangle with diagonals PRPR and QSQS, as shown.Figure 0The value of yy is

Pick one

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 3×25=753\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

Figure for this problem$6.15-$0.75=$5.40. Since 9 chocolates were purchased at the regular price for a total of

Figure for this problem5.40, then the regular price of one chocolate is $5.409=$0.60\frac{\$5.40}{9}=\$0.60 or 60 cents.

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