Let x represent the charge for a book
Let y represent the monthly fee
one month she received 3 books and was charged 74.85. This would be expressed as
3x + y = 74.85
the next month she received 5 books and was charged 116.75. This would be expressed as
5x + y = 116.75
We would solve both equations simultaneously by subtracting the second equation from the first equation. it becomes
3x - 5x + y - y = 74.85 - 116.75
- 2x = - 41.9
x = - 41.9/-2
x = 20.95
We would find y by substituting x = 20.95 into the first equation. It becomes
3(20.95) + y = 74.85
62.85 + y = 74.85
y = 74.85 - 62.85
y = 12
The charge for a book is 20.95
The monthly fee is 12