a collection of nickels, dimes, and quarters consists of 10 coins with a total of $1.45. if the number of dimes is equal to the number of nickels, find the number of each type of coins.

3 nickels, 3 dimes, 4 quarters

Step-by-step 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

3 nickels, 3 dimes, 4 quarters

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