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
[tex]1 \times p + 5 \times n + 25 \times q = 617[/tex]
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
