Plzzzz plz help plz I don’t get it

Mathematics

1 answer:

Morgarella [4.7K]3 years ago

7 0

$\bf \begin{cases}
r=\textit{Richard's bookmarks amount}\\
R=\textit{Rose's bookmarks amount}\\[-0.5em]
\hrulefill\\
\stackrel{\textit{but we know their amount is the same}}{r=R}
\end{cases}~\hspace{5em}
\begin{array}{llll}
\stackrel{\textit{Richard gave away 28}}{r-28}\\\\
\stackrel{\textit{Rose threw away 16}}{R-16}
\end{array}
\\\\[-0.35em]
\rule{34em}{0.25pt}$

$\bf \stackrel{\textit{after they got rid of those, the ratio r:R is 2:5}}{\cfrac{\textit{Richard new amount}}{\textit{Rose new amount}}\qquad \cfrac{r-28}{R-16}=\cfrac{2}{5}}~\hspace{5em}\stackrel{\textit{since we know r=R}}{\cfrac{r-28}{r-16}=\cfrac{2}{5}}
\\\\[-0.35em]
~\dotfill\\\\
5(r-28)=2(r-16)\implies 5r-140=2r-32\implies 3r=108
\\\\\\
r=\cfrac{108}{3}\implies \blacktriangleright r=36=R \blacktriangleleft$

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