There are 16 quarters in the bank
Explanations:Let the number of quarters be represented as q
Let the number of dimes be represented as d
Note that:
1 dime = $0.1
1 quarter = $0.25
The total value of quarters and dimes is $5.20
This can be interpreted mathematically as:
0.1d + 0.25q = 5.20.................(1)
If the quarters were dime and the dime were quarters, the total coins would be $4.60
This means that:
q = d
d = q
0.1q + 0.25d = 4.60
0.25d + 0.1q = 4.60...........(2)
Multiply equation (1) by 25 and equation (2) by 10
2.5d + 6.25q = 130..........(3)
2.5d + q = 46..........(4)
Subtract equation (4) from equation(3)
5.25q = 84
q = 84/5.25
q = 16
Substitute q = 16 into equation (1)
0.1d + 0.25(16) = 5.20
0.1d + 4 = 5.20
0.1d = 5.20 - 4
0.1d = 1.2
d = 1.2 / 0.1
d = 12
Therefore, there are 16 quarters and 12 dimes in the bank
