Question

Hannah has $3.10 in her piggy bank in nickels and quarters. If there are 22 coins in her piggy bank, how many are nickels and how many are quarters? Please explain and show work.

Answer 1

`12\ nickel`

`10\ quarter`

Explanation:

we know that

`1\ nickel=\$0.05`

`1\ quarter=\$0.25`

Let

x------> the number of nickel coins

y-----> the number of quarter coins

we know that

`x+y=22`

`x=22-y` -----> equation A

`0.05x+0.25y=3.10` ----> multiply by 100 both sides

`5x+25y=310` -----> equation B

Substitute equation A in equation B and solve for y

`5(22-y)+25y=310`

`110y-5y+25y=310`

`20y=310-110`

`20y=200`

`y=10\ quarter`

`x=22-y` ------>
`x=22-10=12\ nickel`