Question

the ratio of dimes to pennies in a purse if 3 to 4. if 3 pennies are taken out of the purse, the ratio of dimes to pennies becomes 1 to 1. how many dimes are in the purse

Answer 1

d/p=3/4

d/(p-3)=1/1

Answer 2

\[\frac{d}{p}=\frac{3}{4}\]

\[4d=3p\]

\[d=\frac{3p}{4}\]

and we also have
\[\frac{d}{p-3}=1\]

\[d=p-3\]

but d=3p/4

\[\frac{3p}{4}=p-3\]
\[\frac{3p}{4}-p=-3\]

\[\frac{3p}{4}-\frac{4p}{4}=-3\]
\[\frac{-1}{4}p=-3\]
\[p=-3(-4)=12\]

so d=p-3=12-3=9

Answer 3

9 dimes are in the purse