Track / Stage 1 / 232 of 320 #232 of 2604

Problem 232

Algebra Difficulty 1.4 Multiple choice CEMC Pascal · Canada · 2026

Max was given $b$ books. In
March, he read one third of these books. In April, he read $5$ more of the books. Max then had $7$ books left to read. If Max never read
the same book more than once, what is the value of $b$ ?

Pick one

Official solutions — 2

Solution 1

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

Solution 2

Max then had $7$ books left to read
and so $\dfrac23b-5=7$ .

Solving, we get $\dfrac23b=12$ or
$2b=12\times3$ and so $b=\dfrac{36}{2}=18$ .

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