In his piggy bank, neil has three times as many dimes as nickels and he has four more quarters than nickels. the coins total are 4.60. how many of each coin does he have?

Neil has 10 quarters, 6 nickels and 18 dimes.

Step-by-step explanation: Suppose the quantity of dimes Neil has is represented by D, the quantity of nickels is N and of quarters is Q.

Neil has three times as many dimes as nickels, so:

D = 3N (1)

Four more quarters than nickels, so:

N = Q - 4 (2)

And the sum of the valor the coins is 4.6:

0.1D + 0.05N + 0.25Q = 4.6 (3)

To solve it, substitute (2) in (1):

D = 3(Q - 4)

D = 3Q - 12 (4)

Now, using (2) and (4), substitute in (3):

0.1(3Q - 12) + 0.05(Q - 4) + 0.25Q = 4.6

0.3Q + 0.05Q + 0.25Q = 4.6 + 1.2 + 0.2

0.6Q = 6

Q = 10

With Q, find N:

N = 10 - 4

N = 6

With N:

D = 3.6

D = 18

Neil has 10 quarters, 6 nickels and 18 dimes.

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: )