Question

John spent $10.50 on 5 notebooks and 6 pens, Ariana spent $8.20 on 4 notebooks and 4 pens. What is the cost of 1 notebook, and what is the cost of 1 pen?

Answer 1

To determine the cost of one notebook and one pen, set up a system of equations from the given purchases, simplify, and solve using substitution or elimination methods to find the values of each individual item.

Step-by-step explanation:

To find the cost of one notebook and one pen based on the information provided, we can set up a system of linear equations. Let's denote the cost of one notebook as n and the cost of one pen as p. We are given two scenarios:

• John spent $10.50 on 5 notebooks and 6 pens, which gives us the equation: 5n + 6p = 10.50.
• Ariana spent $8.20 on 4 notebooks and 4 pens, leading to the equation: 4n + 4p = 8.20.

We can simplify Ariana's equation by dividing each term by 4, which gives us: n + p = 2.05. With this simplified equation and the original equation from John's purchase, we can now solve the system of equations using either substitution or elimination method. Let's use the substitution method:

1. Rewrite Ariana's equation to isolate one variable. If n + p = 2.05, we can solve for n: n = 2.05 - p.
2. Substitute the expression for n into John's equation: 5(2.05 - p) + 6p = 10.50.
3. Simplify and solve for p to find the cost of one pen.
4. Once we have the value of p, we can plug it back into either equation to find the cost of one notebook.

By solving the equations, we would obtain the individual costs of a notebook and a pen.