Question

At a vegetable stand, a person can buy 2 bags of apples and 2 bags of potatoes for $11. At a farmer’s market, the same person can buy 2 bags of apples and 3 bags of potatoes for $13. Assuming the prices are the same, what is the price of each bag of apples and each bag of potatoes? Use the matrix equation to solve the system of equations. A matrix with 2 rows and 2 columns where row 1 is 2 and 2, and row 2 is 2 and 3, multiplied by a matrix with 2 rows and 1 column where row 1 is a and row 2 is p equals a matrix with 2 rows and 1 column where row 1 is 11 and row 2 is 13. A matrix with 2 rows and 1 column where row 1 is 2.75 and row 2 is 2.17. A matrix with 2 rows and 1 column where row 1 is 3.5 and row 2 is 2. A matrix with 2 rows and 1 column where row 1 is 4 and row 2 is 6. A matrix with 2 rows and 1 column where row 1 is 7 and row 2 is 8.

Answer 1

To determine the price of each bag of apples and potatoes, we form a system of equations and represent it using matrices. After solving the matrix equation, we find that the price of a bag of apples is $2.75 and the price of a bag of potatoes is $2.17.

Step-by-step explanation:

To solve for the price of each bag of apples and each bag of potatoes, we can represent the given information as a system of linear equations and use matrix algebra to find the solution. The two equations based on the information provided are:

• 2a + 2p = 11 (from the vegetable stand)
• 2a + 3p = 13 (from the farmer’s market)

We can write this system as a matrix equation:

[2 2] [a][2 3] x [p] = [11]
[13]

To solve for 'a' (the price of apples) and 'p' (the price of potatoes), we need to find the inverse of the coefficient matrix and multiply it by the matrix containing the totals spent. Once we do this calculation, the resulting matrix will give us the values for 'a' and 'p'.

After performing the matrix calculations, we find that:

• a = 2.75 (price of a bag of apples)
• p = 2.17 (price of a bag of potatoes)