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Little Billie breaks open his piggy bank and finds that he has 261 coins. There are 10 pennies, 1 nickel, and the rest are all dimes a quarters. His net coinage is 39.40. How many dimes and quarters did he have?(slove by systems of equations)d+q=250.10d+.25q=39.40

Respuesta :

The system of equations to solve:

[tex]\begin{gathered} d+q=250 \\ 0.1d+0.25q=39.40 \end{gathered}[/tex]

Let's solve the first equation for d:

[tex]\begin{gathered} d+q=250 \\ d=250-q \end{gathered}[/tex]

Now, we can substitute this into the second equation and solve for q. Steps are shown:

[tex]\begin{gathered} 0.1d+0.25q=39.40 \\ 0.1(250-q)+0.25q=39.40 \\ 25-0.1q+0.25q=39.40 \\ 0.15q=39.40-25 \\ 0.15q=14.4 \\ q=\frac{14.4}{0.15} \\ q=96 \end{gathered}[/tex]

Let's solve for d:

[tex]\begin{gathered} d+q=250 \\ d+96=250 \\ d=250-96 \\ d=154 \end{gathered}[/tex]Answer

Number of Dimes = 154

Number of Quarters = 96

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