We need to find the two equations that represents the total amount of coins Carl has that makes $26.00 and the number of quarters and dimes.
Carl has 35 dimes and 90 quarters. The equations are [tex]0.1x+0.25y=26[/tex] and [tex]x+y=125[/tex].
Let the number of dimes be [tex]x[/tex]
Let the number of quarters be [tex]y[/tex]
The total number of coins is [tex]125[/tex]
So, the first equation will be
[tex]x+y=125[/tex]
The value of the coins is $26. So,
[tex]0.1x+0.25y=26[/tex]
Let us solve the equations
[tex]x=125-y[/tex]
[tex]0.1\times (125-y)+0.25y=26\\\Rightarrow 12.5-0.1y+0.25y=26\\\Rightarrow 0.15y=13.5\\\Rightarrow y=\dfrac{13.5}{0.15}\\\Rightarrow y=90[/tex]
[tex]x+y=125\\\Rightarrow x=125-90\\\Rightarrow x=35[/tex]
The number of dimes is 35 and the number of quarters is 90.
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