Answer:
There are 25 nickels, 20 dimes and 40 quarters
Step-by-step explanation:
Let
x ----> the number of nickels coins
y ----> the number of dimes coins
z ---> the number of quarters coins
Remember that
[tex]1\ nickel=\$0.05\\1\ dime=\$0.10\\1\ quarter=\$0.25[/tex]
we know that
[tex]x+y+z=85[/tex] ----> equation A
[tex]0.05x+0.10y+0.25z=13.25[/tex] ----> equation B
[tex]z=2y[/tex] ----> equation C
Substitute equation C in equation A and equation B
[tex]x+y+2y=85[/tex]
[tex]x+3y=85[/tex] -----> equation D
[tex]0.05x+0.10y+0.25(2y)=13.25[/tex]
[tex]0.05x+0.60y=13.25[/tex] -----> equation E
Solve the system of equations D and E by graphing
Remember that the solution of the system is the intersection point both graphs
The solution is the point (25,20)
see the attached figure
Find the value of z
[tex]z=2y\\z=2(20)=40[/tex]
therefore
There are 25 nickels, 20 dimes and 40 quarters
