Power Standard 7: Real world problemsA local organic farmer sold 8 boxes of peaches and 6 boxesof tomatoes to one customer for $82. A second customerpurchased 6 boxes of peaches and 7 boxes of tomatoes. Shespent $79. How much did a box of peaches and a box oftomatoes cost? Write and solve a system of equations. Showyour steps.

Peaches cost $5 and Tomatoes cost $7 per box.

Step-by-step explanation:

Let p be the price per box of peaches and t the price of a box of tomatoes. So we have the system:

8p + 6t = 82

6p + 7t = 79

Multiply the first equation by 3 and the second by - 4:

24p + 18t = 246

-24p - 28t = - 316 Adding:

- 10t = - 70

t = 7

Substituting for t in the first equation:

8p + 6 (7) = 82

8p = 40

p = 5.