Question

A grocery store sells bananas for dollars a pound and grapes for dollars a pound. Devren buys 3 pounds of bananas and 4 pounds of grapes for $10.25. Stacey buys 2 pounds of bananas and 2 pounds of grapes for $5.50.

(a) Write the system that represents this situation.

(b) Solve the system. How much is a pound of bananas? How much is a pound of grapes?

Answer 1

Explanation:

Let the price of each pounds of bananas be x andthe price of each pounds of grapes be y.

ATQ,

3x+4y = 10.25 ...(1)

2x+2y = 5.5 ..(2)

Multiply equation (2) by 2.

4x+4y = 11 ...(3)

Now, subtract equation (1) from (3).

4x+4y-(3x+4y) = 11-10.25

4x+4y-3x-4y = 0.75

x = 0.75

Put the value of x in equation (2)

2(0.75)+2y = 5.5

1.5+2y = 5.5

2y = 5.5 - 1.5

2y = 4

y = 2

So, there are 0.75 pounds of bananas and 2 pounds of grapes.