Question

Diana purchased 6 pounds of strawberries and 4 pounds of apples for $18.90. Then she realized that this was not enough and purchased 3 more pounds of each fruit for $10.74. What was the cost per pound for each type of fruit?

Answer 1

The strawberries cost $2.29 per pound and the apples cost $1.29 per pound.

Explanation:

Based on the question, we can assume that the cost per pound of each type of fruit is constant, meaning that the cost per pound of strawberries for the 6 pounds of strawberries is the same as the cost per pound of strawberries for the additional 3 pounds Diana bought after realizing she did not buy enough.

To solve this problem, we need to set up our system of equations:
Let `t` be the cost per pound for strawberries and `a` be the cost per pound of apples.
For both purchases, we can write the equations in word form:
(pounds of strawberries)(cost per pound of strawberries) + (pounds of apples)(cost per pound of apples) = (total cost of purchase)

For her initial purchase:
`6t+4a=18.9`
For the second purchase:
`3t+3a=10.74`

Using this system of equations of two equations and two variables, we can solve for `t` and `a`. To use elimination, we first double the second equation:
`6t+6a=21.48`
Then subtract the first equation from this modified second equation:
`6t+6a-(6t+4a)=21.48-18.9`
`6t+6a-6t-4a=2.58`
`2a=2.58`
`a=1.29`

To find t, we can substitute this value of `a` into `6t+4a=18.9` and solve for `t`:
`6t+4(1.29)=18.9`
`6t=18.9-4(1.29)`
`6t=13.74`
`t=2.29`

Therefore, the strawberries cost $2.29 per pound and the apples cost $1.29 per pound.