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.

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

a.)the line for function b is steeper

$113.42

i hope that is right.

step-by-step explanation: