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Problem 232

Algebra Difficulty 1.4 Multiple choice CEMC Pascal · Canada · 2026

Max was given bb books. In March, he read one third of these books. In April, he read 55 more of the books. Max then had 77 books left to read. If Max never read the same book more than once, what is the value of bb?

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Official solutions — 2

Solution 1

In March, Max read 13\frac13 of the bb books, meaning that he had 1−13=231-\dfrac13=\dfrac23 of the bb books, or 23b\dfrac23b books, left to read. In April, he read 55 more books, thus leaving 23b−5\dfrac23b-5 books left to read. Max then had 77 books left to read and so 23b−5=7\dfrac23b-5=7. Solving, we get 23b=12\dfrac23b=12 or 2b=12×32b=12\times3 and so b=362=18b=\dfrac{36}{2}=18.

Solution 2

In March, Max read 13\frac13 of the bb books, meaning that he had 1−13=231-\dfrac13=\dfrac23 of the bb books, or 23b\dfrac23b books, left to read. In April, he read 55 more books, thus leaving 23b−5\dfrac23b-5 books left to read. Max then had 77 books left to read and so 23b−5=7\dfrac23b-5=7. Solving, we get 23b=12\dfrac23b=12 or 2b=12×32b=12\times3 and so b=362=18b=\dfrac{36}{2}=18.

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