Question

She bought a total of 7 cans at a cost of $21.50. Each can of pears cost $3.20, and each can of mixed fruit cost $2.90. How many cans of pears did she buy? How many cans of mixed fruit did she buy?

Answer 1

The problem can be solved by setting up a system of linear equations. After solving the equations, it is determined that the student bought 4 cans of pears and 3 cans of mixed fruit.

Step-by-step explanation:

The student's question is asking us to solve for the number of cans of pears and mixed fruit she bought given the total cost and the price per can of each fruit. This is a classic linear system of equations problem that can be solved using algebra.

Let's denote the number of cans of pears as p and the number of cans of mixed fruit as f. We have two pieces of information:

• She bought a total of 7 cans: p + f = 7
• The total cost of the cans is $21.50: 3.20p + 2.90f = 21.50

We can solve these equations simultaneously to find the values of p and f.

From the first equation, f = 7 - p. Substituting f in the second equation, we get 3.20p + 2.90(7 - p) = 21.50.

Solving this equation:
3.20p + 20.30 - 2.90p = 21.50
0.30p = 1.20
p = 4

Therefore, she bought 4 cans of pears. Using the first equation again, f = 7 - 4 = 3, so she bought 3 cans of mixed fruit.

In summary, the student bought 4 cans of pears and 3 cans of mixed fruit.