Question

Your friend claimed she has a bag of 30 coins containing nickels, dimes and quarters. The total value of the 30 coins is $2. There are twice as many nickels as there are dimes. Is your friend correct? Explain your reasoning.

Answer 1

Answer:

There are 20 nickels and 10 dimes

The friend is correct, there are twice as many nickels as there are dimes

Step-by-step explanation:

Let

x -----> the number of nickels

y -----> the number of dimes

z ----> the number of quarters

Remember that

1 nickel=$0.05

1 dime=$0.10

1 quarter=$0.25

so

x+y+z=30 -----> equation A

0.05x+0.10y+0.25z=2

Multiply by 100 both sides

5x+10y+25z=200 -----> equation B

x=2y ----> equation C

substitute equation C in equation A and equation B

2y+y+z=30 -----> 3y+z=30 -----> equation D

5(2y)+10y+25z=200 ----> 20y+25z=200 ----> equation E

Solve the system of equations D and E by graphing

The solution is the point (0,10)

z=0, y=10

see the attached figure

Find the value of x

x=2y -----> x=2(10)=20

therefore

There are 20 nickels and 10 dimes

The friend is correct, there are twice as many nickels as there are dimes