Question

A child has $6.17 in change in her piggy bank. The change consists of 113 coins in a mix of pennies, nickels and quarters. If there are 8 times as many nickels as pennies, how many of each coin does the child have

Answer 1

There are 12 pennies, 96 nickels and 5 quarters in piggy bank

Solution:

Let "p" be the number of pennies

Let "n" be the number of nickels

Let "q" be the number of quarters

We know that,

1 penny = 1 cent

1 nickel = 5 cents

1 quarter = 25 cents

The change consists of 113 coins in a mix of pennies, nickels and quarters

Therefore,

p + n + q = 113 ----------- eqn 1

There are 8 times as many nickels as pennies

Number of nickels = 8 times number of pennies

n = 8p ------------ eqn 2

A child has $6.17 in change in her piggy bank

$ 6.17 = 617 cents

Therefore, we frame a equation as:

1 penny x number of pennies + 1 nickel x number of nickel + 1 quarter x number of quarters = 617

$1 \times p + 5 \times n + 25 \times q = 617$

p + 5n + 25q = 617 ---------- eqn 3

Let us solve eqn 1 , eqn 2, and eqn 3

Substitute eqn 2 in eqn 1

p + 8p + q = 113

9p + q = 113

q = 113 - 9p ---------- eqn 4

Substitute eqn 2 in eqn 3

p + 5(8p) + 25q = 617

41p + 25q = 617  -------- eqn 5

Substitute eqn 4 in above eqn 5

41p + 25(113 - 9p) = 617

41p + 2825 - 225p = 617

184p = 2208

Divide both sides of equation by 2208

p = 12

Substitute p = 12 in eqn 4

q = 113 -9(12)

q = 113 - 108

q = 5

Substitute p = 12 in eqn 2

n = 8(12)

n = 96

Thus there are 12 pennies, 96 nickels and 5 quarters in piggy bank