Question

In a piggy bank, the number of nickles is 8 more than half the number of quarters. The value of the coins is $21.85. Determine the number of nickels.

Answer 1

To determine the number of nickels in the piggy bank, we can set up a equation using the given information. By solving the equation, we can find the value of x, which represents the number of quarters. Substituting this value back into the expression x/2 + 8 will give us the number of nickels.

Step-by-step explanation:

Let's say the number of quarters in the piggy bank is x.

The number of nickels is 8 more than half the number of quarters, so it is x/2 + 8.

The value of the coins in the piggy bank is $21.85, which can be written as 2185 cents.

The value of each quarter is 25 cents, so the total value of quarters is 25x cents.

The value of each nickel is 5 cents, so the total value of nickels is 5(x/2 + 8) cents.

Equating the total value of quarters and nickels to 2185 cents, we get the equation:

25x + 5(x/2 + 8) = 2185

Solving this equation will give us the value of x, which represents the number of quarters. Once we find the value of x, we can find the number of nickels by substituting it back into the expression x/2 + 8.

Answer 2

The number of nickels is 47

Step-by-step explanation:

1 nickel is 5 cents while 1 quarter is 25 cents

let the number of nickels be n and the number of quarters be q

From the question;

the number of nickels n is 8 more than half the number of quarters (q/2)

n = q/2 + 8

(n-8) = q/2

q = 2(n-8) = 2n - 16 ••••(i)

let us convert $21.85 to cents

there are 100 cents in $1

Thus; $21.85 will be 21.85 * 100 = 2185 cents

1 nickel is 5 cents; so n nickels will be 5 * n = 5n cents

1 quarter is 25 cents; so q quarters will be 25 * q = 25q cents

The addition of both will give 2185 cents

Thus;

5n + 25q = 2185 ••••••(ii)

Substitute equation i into ii

5n + 25(2n-16) = 2185

5n + 50n - 400 = 2185

55n = 2185 + 400

55n = 2,585

n = 2,585/55

n = 47 nickels