For this case, the first thing we must do is define variables.
We have then:
x: number of pennies
y: number of dimes
z: number of quarters
We now write the system of equations:
the box containts 44 coins:
[tex] x + y + z = 44
[/tex]
The number of pennies is equal to the number of dimes:
[tex] x = y
[/tex]
the total value is $ 4.37:
[tex] 0.01x + 0.1y + 0.25z = 4.37
[/tex]
Solving the system of equations graphically, we obtain:
Let's rewrite equations 1 and 2:
[tex] x + x + z = 44
0.01x + 0.1x + 0.25z = 4.37
[/tex]
The intersection of the straight lines is the graphic solution
Note: see attached image
x = 17
z = 10
Then, the value of y is:
y = x = 17
Answer:
pennies = 17
dimes = 17
Quarters = 10
