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.