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Algebra Difficulty 1.4 Junior Find the answer Canada

There are $186$ students on a
class trip. Each student is placed into exactly one of $50$ groups. Each group has exactly $3$ students or exactly $4$ students. There are $m$ groups that have $3$ students and $n$ groups that have $4$ students. The value of $m-n$ is

Pick one

Solution

There are $50$ groups, and so
$m+n=50$ . There are $186$ students, and so $3m+4n=186$ .

Solving the system of equations, we substitute the first equation $m=50-n$ into the second equation $3m+4n=186$ to get $3(50-n)+4n=186$ .

Solving, we have $150-3n+4n=186$ or
$n=186-150=36$ .

Since $m=50-n=50-36=14$ , then $m-n=14-36=-22$ .

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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.