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Problem 192

Algebra Difficulty 1.7 Multiple choice CEMC Gauss (Grade 8) · Canada · 2014

A bicycle at Store P costs $200. The regular price of the same bicycle at Store Q is 15% more than it is at Store P. The bicycle is on sale at Store Q for 10% off of the regular price. What is the sale price of the bicycle at Store Q?

Pick one

Official solutions — 2

Solution 1

At Store Q, the bicycle’s regular price is $15\%$ more than the price at Store P, or $15\%$ more than $200.

Since $15\%$ of 200 is $\frac{15}{100}\times200=0.15\times200=30$ , then $15\%$ more than $200 is$ \$200+\$30 $or$ \$230$.

This bicycle is on sale at Store Q for 10% off of the regular price, $230.

Since $10\%$ of 230 is $\frac{10}{100}\times230=0.10\times230=23$ , then $10\%$ off of $230 is$ \$230-\$23 $or$ \$207$.
The sale price of the bicycle at Store Q is $207.

Solution 2

The width of Sarah’s rectangular floor is 18 hand lengths.

Since each hand length is 20 cm, then the width of the floor is $18\times20=360$ cm.

The length of Sarah’s rectangular floor is 22 hand lengths.

Since each hand length is 20 cm, then the length of the floor is $22\times20=440$ cm.

Thus the area of the floor is $360\times440=158\,400$ cm $^2$ .
Of the given answers, the closest to the area of the floor is $160\,000$ cm $^2$ .

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