Question

Johir and Ariana bought school supplies. John spent $10.20 on 4 notebooks and 4 pens. Ariana spent $7.00 on 3 notebooks and 2 pens. What is the cost of 1 notebook and what is the cost of 1 pen?

Answer 1

The cost of one notebook is $1.90 and the cost of one pen is $0.65. This was determined by setting up and solving a system of equations based on the purchases made by Johir and Ariana.

Step-by-step explanation:

To determine the cost of one notebook and one pen, we should set up a system of equations based on the information given. We have two equations: one for John's purchase and another for Ariana's purchase.

• Let n represent the cost of one notebook.
• Let p represent the cost of one pen.

John's purchase: 4n + 4p = 10.20

Ariana's purchase: 3n + 2p = 7.00

Now, let's solve the system of equations:

1. Multiply the second equation by 2 to match the number of pens in the first equation: 2 * (3n + 2p) = 2 * 7.00, yielding 6n + 4p = 14.00.
2. Subtract the first equation from this new equation: (6n + 4p) - (4n + 4p) = 14.00 - 10.20, which simplifies to 2n = 3.80.
3. Divide both sides by 2 to find the cost of one notebook: n = 3.80 / 2, so n = 1.90.
4. Now, substitute the value of n back into either of the original equations to find the cost of one pen. Using Ariana's purchase: 3(1.90) + 2p = 7.00 simplifies to 5.70 + 2p = 7.00.
5. Subtract 5.70 from both sides: 2p = 7.00 - 5.70, so 2p = 1.30.
6. Finally, divide by 2 to get the price of one pen: p = 1.30 / 2, so p = 0.65.

Therefore, the cost of one notebook is $1.90 and the cost of one pen is $0.65.