Question

The first customer paid $8.75 for 3 notebooks and 5 pens. The second customer paid $12 for 8 notebooks and 2 pens. What was the cost in dollars of each notebook?

A. $1.25
B. $1.50
C. $1.75
D. $2.00

Answer 1

The cost of each notebook is determined by solving a system of linear equations derived from the information given about the payments made by two customers for notebooks and pens. The calculations reveal that each notebook costs $1.75.

Step-by-step explanation:

The problem presents a system of linear equations where the first customer paid $8.75 for 3 notebooks and 5 pens, and the second customer paid $12 for 8 notebooks and 2 pens. To solve for the price of each notebook, we can set up the system as follows:

1. Let x be the cost of one notebook
2. Let y be the cost of one pen
3. First equation: 3x + 5y = $8.75
4. Second equation: 8x + 2y = $12

To solve the system, we can multiply the first equation by 2 to match the number of pens in the second equation:

1. 6x + 10y = $17.50
2. Subtract the second equation from the one we just obtained to eliminate y:
3. (6x + 10y) - (8x + 2y) = $17.50 - $12
4. (6x - 8x) + (10y - 2y) = $5.50
5. -2x + 8y = $5.50
6. Divide by -2: x = $1.75

Thus, the cost of each notebook is $1.75, which corresponds to option C.