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?

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(22740) (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
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