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
