Question

You have 85 coins

in nickels, dimes, and quarters with a combined value
of $13.25. There are twice as many quarters as dimes.

Answer 1

There are 25 nickels, 20 dimes and 40 quarters

Explanation:

Let

x ----> the number of nickels coins

y ----> the number of dimes coins

z ---> the number of quarters coins

Remember that

`1\ nickel=\$0.05\\1\ dime=\$0.10\\1\ quarter=\$0.25`

we know that

`x+y+z=85` ----> equation A

`0.05x+0.10y+0.25z=13.25` ----> equation B

`z=2y` ----> equation C

Substitute equation C in equation A and equation B

`x+y+2y=85`

`x+3y=85` -----> equation D

`0.05x+0.10y+0.25(2y)=13.25`

`0.05x+0.60y=13.25` -----> 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

`z=2y\\z=2(20)=40`

therefore

There are 25 nickels, 20 dimes and 40 quarters