Question

Ms. Tyler is running the school store, which is running a promotion on school supplies. Different supplies are placed on two shelves. You can purchase 3 items from shelf A and 2 from shelf B for $16. Or you can purchase 2 items from shelf A and 3 from shelf B for $14. Write and solve a system of equations that can be used to find the individual prices for supplies on shelf A and on shelf B.

Answer 1

To solve the problem, create a system of equations with the given information. Solve the system to find the prices of items on shelves A and B.

Step-by-step explanation:

To solve this problem, we can create a system of equations based on the given information. Let's denote the price of an item from shelf A as A, and the price of an item from shelf B as B.

Based on the information given, we have the following equations:

1. 3A + 2B = 16
2. 2A + 3B = 14

We can solve this system of equations to find the values of A and B.

Multiplying the first equation by 2 and the second equation by 3, we get:

1. 6A + 4B = 32
2. 6A + 9B = 42

Subtracting the first equation from the second equation, we get:

5B = 10

B = 2

Substituting the value of B into the first equation, we can solve for A:

3A + 4 = 16

3A = 12

A = 4

Therefore, the price of an item from shelf A is $4, and the price of an item from shelf B is $2.