​A man has 25 coins in his pocket, all of which are dimes and quarters.

​A man has 25 coins in his pocket, all of which are dimes and quarters. If the total value of his change is 415 cents, how many dimes and how many quarters does he have?

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x = number of quarters
y = number of dimes

x + y = 25  {he has 25 coins in his pocket}
25x + 10y = 415 {value of a coin times number of coins equals total value}

-10x - 10y = -250 {multiplied first equation by -10}
25x + 10y = 415 {second equation stays the same}
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15x = 165 {added the two equations}
x = 11   {divided each side by 15}

11 + y = 25 {substituted 11, in for x, into first equation}
y = 14 {subtracted 11 from each side}

11 quarters
14 dimes

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