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18 votes
18 votes
Chi has $11.70 in dimes and quarters. The number of dimes is seven more than three times the number of quarters. How many of each are there?

User Hiroko
by
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1 Answer

20 votes
20 votes

Start writing the corresponding system of equations taking into account that each dime is equal to $0.1 and each quarter is equal to $0.25, let d be the number of dimes and q the number of quarters.

then,


\begin{cases}0.1d+0.25q=11.70 \\ d=3q+7\end{cases}

insert the second equation into the first one


\begin{gathered} 0.1\cdot(3q+7)+0.25q=11.70 \\ \text{solve for q} \\ 0.3q+0.7+0.25q=11.70 \\ 0.55q+0.7=11.7 \\ 0.55q=11.7-0.7 \\ q=(11)/(0.55) \\ q=20 \end{gathered}

find the number of dimes using the number found and the second equation


\begin{gathered} d=3q+7 \\ d=3\cdot20+7 \\ d=60+7 \\ d=67 \end{gathered}

prove the solution using the first equation


\begin{gathered} 0.1d+0.25q=11.7 \\ 0.1\cdot67+0.25\cdot20=11.7 \\ 6.7+5=11.7 \\ 11.7=11.7 \end{gathered}

There are 67 dimes and 20 quarters.

User Nishant Srivastava
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