Answer:
3 nickels, 3 dimes, 4 quarters
Explanation:
Let n, d, and q represent the numbers of nickels, dimes, and quarters, respectively.
n + d + q = 10
The total value is $1.45
0.05n + 0.1d + 0.25q = 1.45
The number of dimes is equal to the number of nickels.
n = d
We have a system of 3 equations.
n + d + q = 10
0.05n + 0.1d + 0.25q = 1.45
n = d
Substitute n for d in the first and second equations.
n + n + q = 10
0.05n + 0.1n + 0.25q = 1.45
2n + q = 10
0.15n + 0.25q = 1.45 (Equation 1)
Solve the first equation for q.
q = 10 - 2n
Substitute 10 - 2n for q in Equation 1.
0.15n + 0.25(10 - 2n) = 1.45
0.15n + 2.5 - 0.5n = 1.45
-0.35n = -1.05
n = 3
d = n = 3
n + d + q = 10
3 + 3 + q = 10
q + 6 = 10
q = 4
Answer: 3 nickels, 3 dimes, 4 quarters