Question

Last week Andrew bought 9 pounds of zucchini and 6 pounds of tomatoes for $21.15 at a farm stand. This week he bought 4 pounds of zucchini and 3 pounds of tomatoes, at the same prices, for $9.83. What is the cost of 1 pounds of zucchini and 1 pound of tomatoes at the farm stand?

Answer 1

z = 1.39

Explanation:

Answer 2

Let the cost of 1 pound of zucchini be 'z' and the cost of 1 pound of tomatoes be 't'. We can set up two equations using the given information:

9z + 6t = 21.15 (equation 1)

4z + 3t = 9.83 (equation 2)

We can solve for 'z' and 't' using the method of substitution:

From equation 2, we can express 4z as 9.83 - 3t:

4z = 9.83 - 3t

Substituting this expression for 4z in equation 1, we get:

9(9.83 - 3t)/4 + 6t = 21.15

Multiplying both sides by 4 to eliminate the fraction, we get:

9(9.83 - 3t) + 24t = 84.6

Expanding the left side, we get:

88.47 - 27t + 24t = 84.6

Combining like terms, we get:

-3t = -3.87

Dividing both sides by -3, we get:

t = 1.29

Substituting this value of 't' in equation 2, we get:

4z + 3(1.29) = 9.83

Simplifying, we get:

4z = 5.56

Dividing both sides by 4, we get:

z = 1.39

Therefore, 1 pound of zucchini costs $1.39 and 1 pound of tomatoes costs $1.29 at the farm stand.