360 dictionaries packed in boxes by 15 or 9

Question

A publisher ordered 2 types of dictionaries: X and Y. They total to 360. One box of X contains 15 dictionaries. One box of Y contains 9 dictionaries. If the publisher received same number of X and Y boxes, how many boxes did the publisher receive?

What equation should I form?

Answer 1

Let $x$ be number of Dictionary type X, $y$ be number of Dictionary type Y.

So: $x+y=360$.

Also, let the number of boxes of dictionary X be equal to $n$. Note that $n$ is also the number of boxes of dictionary Y. So number of dictionaries type X is $15n$, and type Y is $9n$.

So first equation can be written as: $15n+9n=360$, i.e. $n=15$. So total number of boxes is $n+n=30$

(Going one step further than what has been asked, we see that: $x=225$ books, and $y=135$ books)

Answer 2

A pair of $X+Y$ boxes contains $24$ books, so he received $15$ pairs.

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If you really really need an equation,

$$(15+9)p=360.$$