If 40 pounds of tomatoes and 20 pounds of bananas cost $26 and 10 pounds of tomatoes and 50 pounds of bananas cost $20, what is the price per pound of tomatoes and bananas?

A. Tomatoes: $0.40 per pound; Bananas: $0.50 per pound
B. Tomatoes: $0.60 per pound; Bananas: $0.30 per pound
C. Tomatoes: $0.60 per pound; Bananas: $0.10 per pound
D. Tomatoes: $0.50 per pound; Bananas: $0.30 per pound

Question

High School

Answer :

LorraineNoble LorraineNoble · Answer 1 · 2025-05-29T18:50:14-04:00

By solving a system of linear equations, it's found that tomatoes cost $0.50 per pound and bananas cost $0.30 per pound.

The question deals with a system of linear equations to find the price per pound of tomatoes and bananas.

Let t be the price per pound of tomatoes and b be the price per pound of bananas. From the given information, we construct two equations:

Solving this system step by step:

Multiply the first equation by 1/4 to simplify: 10t + 5b = 6.5
Subtract the modified first equation from the second equation to eliminate t: 45b = 13.5
Now, solve for b: b = 13.5 / 45 = $0.30 per pound
Substitute b = $0.30 back into one of the original equations to solve for t. Using 10t + 5(0.30) = 6.5: t = $0.50 per pound

Hence, tomatoes cost $0.50 per pound and bananas cost $0.30 per pound.