SOLUTION: if you have $19.75 and a total of 100 coins, how many dimes is there?

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Question 350705: if you have $19.75 and a total of 100 coins, how many dimes is there?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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if you have $19.75 and a total of 100 coins, how many dimes is there?
:
This solution is based on the fact that you only have dimes and quarters
d = no. dimes
q = no. of quarters
:
The total coin equation
d + q = 100
q = (100-d)
:
The total value equation
.10d + .25q = 19.75
Replace q with (100-d)
.10d + .25(100-d) = 19.75
.10d + 25.00 - .25d = 19.75
.10d - .25d = 19.75 - 25.00
-.15d = -5.25
d = %28-5.25%29%2F%28-.15%29
d = 35 dimes
:
:
to check this, 100 - 35 = 65 quarters
.10(35) + .25(65) =
3.50 + 16.25 = 19.75, confirms our solution of 35 dimes