Question

A piggy bank contains nickels and dimes. There are 160 total coins valuing $10.50. Think about a system of equations that can be used to represent the number of nickels and dimes and then think through using substitution to solve the system of equations. How many nickels are in the piggy bank?
99


1,090


110


1,100

Answer 1

$x + y = 160 \\ 0.05x + 0.1y = 10.50$
First, Substitute x + y = 160 into equation
x = 160 - y
$0.05(160 - y) + 0.1y = 10.50 \\ 8 - 0.05y + 0.1y = 10.50 \\ 0.05y = 2.50 \\ y = 50$
Substitute that into
$x + 50 = 160 \\ x = 110$

The answer is 110.

Hope this helps. - M