Question

a piggy bank has $6.95 and contain only nickels and dimes. If there are a total of 91 coins, how many nickels are there

Answer 1

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

$10(x+y=91)\\10x+10y=910\ \ \ Eqn\ 3$

Subtracting Eqn 2 from Eqn 3

$(10x+10y)-(5x+10y)=910-695\\10x+10y-5x-10y=215\\5x=215$

Dividing both sides by 5

$\frac{5x}{5}=\frac{215}{5}\\x=43$

There are 43 nickels in the piggy bank.

Keywords: linear equation, elimination method

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