Question

Joanna has a total of 50 coins in her purse. The coins are either nickels or quarters. The total value of the coins is $7.10.

Which system of equations can be used to determine the number of nickels, n, and quarters, q, that Joanna has in her purse?

A. n+q+50
0.05n+0.25q=7.10


B. n+q=7.10
50n+50q=7.10

C. 0.05n+0.25q=50
n+q=7.10

D. 0.05n+ 0.25q= 7.10
50n+50q=7.10

Answer 1

Option A.

Explanation:

Let

n-----> the number of nickels

q----> the number of quarters

Remember that

`1\ nickel=\$0.05`

`1\ quarter=\$0.25`

we know that

`n+q=50` ----> equation A

`0.05n+0.25q=7.10` -----> equation B

using a graphing tool-----> solve the system of equations

The solution is the point (27,23)

see the attached figure

therefore

The number of nickels is 27

The number of quarters is 23