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, 2022

Algebra Difficulty 1.6 Junior Find the answer Canada

There are $\frac{2}{3}$ as
many golf balls in Bin F as in Bin G. If there are a total of golf
balls, how many fewer golf balls are in Bin F than in Bin G?

Pick one

Solution

If the value of $P$ is less
than 9, then $QR+PPP+PPP$ is at most
$99+888+888=1875$ .

Since the given sum is 2022, then the value of $P$ cannot be less than 9 and thus must
equal 9.

When $P=9$ , we get $QR+999+999=2022$ , and so $QR=2022-999-999=24$ .

Therefore $Q=2$ , $R=4$ , and so $P+Q+R=9+2+4=15$ .

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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.