Question

An envelope with 96 bookmarks in it has a mass of 1467 grams. The same envelope with 49 bookmarks in it has a mass of 762 grams. Find the mass of the envelope when it is empty.

Answer 1

If
`m` is the mass of the envelope and
`b` the mass of one bookmark, then

`\begin{cases}m+96b=1467\\m+49b=762\end{cases}`

We have

`(m+96b)-(m+49b)=1467-762\implies47b=705\implies b=15`

Then

`m+96\cdot15=1467\implies m+1440=1467\implies m=27`

so the envelope has a mass of 27 grams.