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.

Respuesta :

If [tex]m[/tex] is the mass of the envelope and [tex]b[/tex] the mass of one bookmark, then

[tex]\begin{cases}m+96b=1467\\m+49b=762\end{cases}[/tex]

We have

[tex](m+96b)-(m+49b)=1467-762\implies47b=705\implies b=15[/tex]

Then

[tex]m+96\cdot15=1467\implies m+1440=1467\implies m=27[/tex]

so the envelope has a mass of 27 grams.

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