There are three numbers $m$, $n$, and $p$ such that the sum of $m$ and $n$ is 144, the sum of thrice $n$ and five times $p$ is 464, and the sum of $p$ and $m$ is 160. What is the value of $p$?

Question

Accepted Answer

64. Let $m+n=144$, $3n+5p=464$, and $m+p=160$. Adding the first and third gives $2m+n+p=304$, and using $m=160-p$ and $n=144-m$ leads to a single equation in $p$. Solving gives $p=64$.

There are three numbers $m$, $n$, and $p$ such that the sum of $m$ and $n$ is 144, the sum of thrice $n$ and five times $p$ is 464, and the sum of $p$ and $m$ is 160. What is the value of $p$?

Solution

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