Dimes and Quarters

Gloria has some dimes and quarters. If she has 25 coins worth a total of $3.10, how many of each type of coin does she have?

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x = number of dimes
25 - x = number of quarters

10x + 25(25 - x) = 310 {value of coin times number of coins equals total value/changed dollars to cents}
10x + 625 - 25x = 310 {used distributive property}
-15x + 625 = 310 {combined like terms}
​-15x = -315 {subtracted 625 from each side}
x = 21 {divided each side by -15}
25 - x = 4 {substituted 21, in for x, into 25 - x}

21 dimes and 4 quarters

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