Question

Carl collects coins compulsively, but he only likes quarters and dimes. Carl currently has 125 coins for a total of $26.00. How many of each coin does Carl have? What are the two equations?
0.25x + 0.1y = 1
0.25x + 0.1y = 2
0.1x + 0.25 = 26
x + y = 125
x + y = 26

Answer 1

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 $0.1x+0.25y=26$ and $x+y=125$.

Let the number of dimes be $x$

Let the number of quarters be $y$

The total number of coins is $125$

So, the first equation will be

$x+y=125$

The value of the coins is $26. So,

$0.1x+0.25y=26$

Let us solve the equations

$x=125-y$

$0.1\times (125-y)+0.25y=26\\\Rightarrow 12.5-0.1y+0.25y=26\\\Rightarrow 0.15y=13.5\\\Rightarrow y=\dfrac{13.5}{0.15}\\\Rightarrow y=90$

$x+y=125\\\Rightarrow x=125-90\\\Rightarrow x=35$

The number of dimes is 35 and the number of quarters is 90.

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