# SOLUTION: In Anna's pocket, there is \$16.20 in quarters, nickels, and dimes. In all, there are 97 coins. If there are seven more nickels than dimes, find how many of each kind there are?

Algebra ->  Algebra  -> Finance -> SOLUTION: In Anna's pocket, there is \$16.20 in quarters, nickels, and dimes. In all, there are 97 coins. If there are seven more nickels than dimes, find how many of each kind there are?      Log On

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 Question 439808: In Anna's pocket, there is \$16.20 in quarters, nickels, and dimes. In all, there are 97 coins. If there are seven more nickels than dimes, find how many of each kind there are?Answer by ankor@dixie-net.com(15649)   (Show Source): You can put this solution on YOUR website!let n = no. of nickels let d = no. of dimes let q = no. of quarters ; Write an equation for each statement: : "In Anna's pocket, there is \$16.20 in quarters, nickels, and dimes." .05n + .10d + .25q = 16.20 : " In all, there are 97 coins." n + d + q = 97 : "If there are seven more nickels than dimes," n = (d+7) : Multiply the 1st equation by 4, subtract from the total coin equation: 1n + 1d + 1q = 97 .2n + .4n + q = 64.8 --------------------Subtraction eliminates q .8n + .6d = 32.20 : n = (d+7), replace n with (d+7) in the above equation, find d .8(d+7) + .6d = 32.20 .8d + 5.6 + .6d = 32.20 .8d + .6d = 32.20 - 5.6 1.4d = 26.6 d = d = 19 dimes then we know n = (d+7), therefore: n = 19 + 7 n = 26 nickels : Find q using the total coin equation: 26 + 19 + q = 97 q = 97 - 45 q = 52 quarters : Check solutions in the total value equation .05(26) + .10(19) + .25(52) = 1.30 + 1.90 + 13 = 16.20, confirms our solutions : : find how many of each kind there are? 26 nickels, 19 dimes and 52 quarters