There are 43 nickels in the piggy bank.
Step-by-step explanation:
Given,
Amount in piggy bank = $6.95 = 6.95*100 = 695 cents
Total coins = 91
One nickel = 5 cents
One dime = 10 cents
Let,
x be the number of nickels
y be the number of dimes
According to given statement;
x+y=91 Eqn 1
5x+10y=695 Eqn 2
Multiplying Eqn 1 by 10
[tex]10(x+y=91)\\10x+10y=910\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 2 from Eqn 3
[tex](10x+10y)-(5x+10y)=910-695\\10x+10y-5x-10y=215\\5x=215[/tex]
Dividing both sides by 5
[tex]\frac{5x}{5}=\frac{215}{5}\\x=43[/tex]
There are 43 nickels in the piggy bank.
Keywords: linear equation, elimination method
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