Let x represent the number of $5 dollar bills
Let y represent the number of $10 dollar bills
Let z represent the number of $20 dollar bills
The wallet contained 11 bills in total. This means that
x + y + z = 11 (first equation)
The total value of the $5 bills is 5x
The total value of the $10 bills is 10y
The total value of the $20 bills is 20z
Given that the total value of the bills is $115, it means that
5x + 10y + 20z = 115 (second equation)
The total amount of the $5 and $10 was $75. It means that
5x + 10y = 75 (Third equation)
From the first equation,
x = 11 - y - z
Substituting this equation into the second and third equation, it becomes
5(11 - y - z) + 10y + 20z = 115
55 - 5y - 5z + 10y + 20z = 115
- 5y + 10y - 5z + 20z = 115 - 55
5y + 15z = 60 (equation 4)
5(11 - y - z) + 10y = 75
55 - 5y - 5z + 10y = 75
- 5y + 10y - 5z = 75 - 55
5y - 5z = 20
y - z = 4
y = 4 + z
Substituting y = 20 + z into the 4th equation, it becomes
5(4 + z) + 15z = 60
20 +5z + 15z = 60
5z + 15z = 60 - 20
20z = 40
z = 40/20
z = 2
y = 4 + z = 4 + 2 = 6
x = 11 - y - z = 11 - 6 - 2
x = 3
The $5 bills were 3
The $10 bills were 6
The $20 bills were 2