CEMC Pascal, 2024

Algebra Difficulty 1.4 Junior Find the answer Canada

Lauren plays basketball with her friends. She makes $10$ baskets. Each of these baskets is
worth either $2$ or $3$ points. Lauren scores a total of $26$ points. How many $3$ point baskets did she make?

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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