Trish made a few pans of Brownies to sell. Rachel also contributed 5 pans. Each pan of brownies was cut into 12 squares. If ther
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There are 12 pennies, 96 nickels and 5 quarters in piggy bank
<em><u>Solution:</u></em>
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
<em><u>The change consists of 113 coins in a mix of pennies, nickels and quarters</u></em>
Therefore,
p + n + q = 113 ----------- eqn 1
<em><u>There are 8 times as many nickels as pennies</u></em>
Number of nickels = 8 times number of pennies
n = 8p ------------ eqn 2
<em><u>A child has $6.17 in change in her piggy bank</u></em>
$ 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
p + 5n + 25q = 617 ---------- eqn 3
<em><u>Let us solve eqn 1 , eqn 2, and eqn 3</u></em>
<em><u>Substitute eqn 2 in eqn 1</u></em>
p + 8p + q = 113
9p + q = 113
q = 113 - 9p ---------- eqn 4
<em><u>Substitute eqn 2 in eqn 3</u></em>
p + 5(8p) + 25q = 617
41p + 25q = 617 -------- eqn 5
<em><u>Substitute eqn 4 in above eqn 5</u></em>
41p + 25(113 - 9p) = 617
41p + 2825 - 225p = 617
184p = 2208
Divide both sides of equation by 2208
<h3>p = 12</h3><em><u>Substitute p = 12 in eqn 4</u></em>
q = 113 -9(12)
q = 113 - 108
<h3>q = 5</h3><em><u>Substitute p = 12 in eqn 2</u></em>
n = 8(12)
<h3>n = 96</h3>Thus there are 12 pennies, 96 nickels and 5 quarters in piggy bank