There are 29 nickles in the pile.
Step-by-step explanation:
Let,
nickles = x
dimes = y
Total coins = 82
Total worth = $6.75 = 6.75*100 = 675 cents
1 nickle = 5 cents
1 dime = 10 cents
According to given statement;
x+y=82 Eqn 1
5x+10y=675 Eqn 2
Multiplying Eqn 1 by 5;
[tex]5(x+y=82)\\5x+5y=410\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 3 from Eqn 2
[tex](5x+10y)-(5x+5y)=675-410\\5x+10y-5x-5y=265\\5y=265[/tex]
Dividing both sides by 5;
[tex]\frac{5y}{5}=\frac{265}{5}\\y=53[/tex]
Putting y=53 in Eqn 1
[tex]x+53=82\\x=82-53\\x=29[/tex]
There are 29 nickles in the pile.
Keywords: linear equations, subtraction
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