SOLUTION: A coin bank contains only qurarters and dimes. The total value of the coins is $10.40. If the dimes were quarters and the quarters were dimes the total value of the coins would be

Question 177887: A coin bank contains only qurarters and dimes. The total value of the coins is $10.40. If the dimes were quarters and the quarters were dimes the total value of the coins would be $9.20. Find the total number of dimes in the bank.
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Let d = dimes
and q = quarters
.
Since we have two unknowns we'll need two equations.
.
From: "The total value of the coins is $10.40."
.10d + .25q = 10.40 (equation 1)
.
From: "If the dimes were quarters and the quarters were dimes the total value of the coins would be $9.20"
.25d + .10q = 9.20 (equation 2)
.
Using Cramer's rule:
Determinant of coefficients:
(.10)(.10)-(.25)(.25)
=(0.01)-(0.0625)
=-0.0525
.
Determinant of d:
(10.40)(.10)-(9.20)(.25)
=(1.04)-(2.3)
=-1.26
.
Determinant of q:
(.10)(9.20)-(.25)(10.40)
=(.10)(9.20)-(.25)(10.40)
=(.92)-(2.6)
= -1.68
.
d = Detd/DetCoeff
d = -1.26/-0.0525
d = 24 (number of dimes)
.
q = Detq/DetCoeff
q = -1.68/-0.0525
q = 32 (number of quarters)
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