Question

You have been saving money in a piggy bank. Your piggy bank contains 75 coins that are all nickels and dimes. You take the money out of the bank to count, and find out that you have $5.95 saved up. How many dimes and how many nickels do you have?

Answer 1

You have 31 nickels and 44 dimes.

Step-by-step explanation:

Total coins = 75

Worth of coins = $5.95 = 5.95*100 = 595 cents

1 nickel = 5 cents

1 dime = 10 cents

Let,

Number of nickels = x

Number of dimes = y

According to given statement;

x+y=75   Eqn 1

5x+10y=595    Eqn 2

Multiplying Eqn 1 by 5

$5(x+y=75)\\5x+5y=375\ \ \ Eqn\ 3$

Subtracting Eqn 3 from Eqn 2

$(5x+10y)-(5x+5y)=595-375\\5x+10y-5x-5y=220\\5y=220$

Dividing both sides by 5

$\frac{5y}{5}=\frac{220}{5}\\y=44$

Putting y=44 in Eqn 1

$x+44=75\\x=75-44\\x=31$

You have 31 nickels and 44 dimes.

Keywords: linear equations, subtraction

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