Coin Problem

Ruth emptied her bank.  She found that she had 84 coins all nickels and dimes. The value of the coins was 7.15. How many dimes did she have?

- 84 coins in nickels and dimes
- value was $7.15

x = number of nickels
84 - x = number of dimes {there were 84 coins in all}

5x + 10(84 - x) = 715 {number of coins times value of coins equals total value}
5x + 840 - 10x = 715 {used distributive property}
-5x + 840 = 715 {combined like terms}
-5x = -125 {subtracted 840 from both sides}
x = 25 {divided both sides by -5}
84 - x = 59 {substituted 25, in for x, into 84 - x}

25 nickels and 59 dimes

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