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Algebra Difficulty 2.4 Junior Find the answer Canada

In the subtraction of the two-digit numbers shown, the letters
$P$ and $Q$ each represent a single digit.

The value of $P+Q$ is

Pick one

Solution

We rearrange the given subtraction to create the addition
statement $Q6+49=8P$ .

Next, we consider the units digits.

From the statement, the sum $6+9$ has
a units digit of $P$ which means that
$P=5$ (since $6+9=15$ ). Therefore, we have $Q6+49=85$ .

Rearranging this equation, we get $Q6=85-49=36$ , and so $Q=3$ .

Therefore, $P+Q=5+3=8$ .

(We can check that $85-36=49$ , as
required.)

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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.