Question 745011
There are 52 coins in a purse.  Some of them are quarters, and some are dimes. 
The total value of all coins is $7.45. how many were quarters and how many were dimes?


x = number of quarters
52 - x = number of dimes {there are 52 coins total}


0.25x + 0.1(52 - x) = 7.45 {number of coins times value of coin equals total value}
0.25x + 5.2 - 0.1x = 7.45 {used distributive property}
0.15x + 5.2 = 7.45 {combined like terms}
0.15x = 2.25 {subtracted 5.2 from each side}
x = 15 {divided each side by 0.15}
52 - x = 37 {substituted 15, in for x, into 52 - x}


15 quarters and 37 dimes in the purse
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