Solution
For this case we can create the following notation:
P = number of Pennies
D= number of dimes
Q= number of quarters
The total of coins are 29 so we have this:
P+Q+D= 29 (1)
The total amount is given by:
2.57 = 0.01* P+ 0.1*D + 0.25 Q (2)
We also know that P =D then solving for Q we have:
Q = 29 -P P= 29-2P = 29-2D
Replacing in the second equation we got:
2.57= 0.01D+ 0.1D +0.25(29 -2D)
2.57 = 0.11D + 7.25-0.5 D
(0.5-0.11) D=7.25-2.57
D = 4.68/0.39 = 12
Then P =12
And Q = 29 -(2*12)= 29-24= 5
Then the final answer is:
12 Dimes, 12 Pennies, 5 Quarters
