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

Answer:

(a)

$3b + 4g =10.25$

$2b + 2g = 5.50$

(b)

1 pound of banana = $0.75

1 pound of grape = $2.00

Step-by-step explanation:

Given

Represent banana with b and grapes with g.

From the first statement, we have:

$3b + 4g =10.25$

From the second, we have:

$2b + 2g = 5.50$

Solving (a): The equations

This has been solved above.

The equations are:

$3b + 4g =10.25$

$2b + 2g = 5.50$

Solving (b):

$3b + 4g =10.25$ --- (1)

$2b + 2g = 5.50$ --- (2)

Multiply (2) by 2

$2b + 2g = 5.50$ * 2

$4b + 4g = 11$ ----- (3)

Subtract (3) from (1)

$3b - 4b + 4g - 4g = 10.25 - 11$

$-b =-0.75$

$b =0.75$

Substitute 0.75 for b in (2)

$2b + 2g = 5.50$

$2 *0.75 + 2g = 5.5$

$1.5 + 2g = 5.5$

Collect Like Terms

$2g = 5.5 - 1.5$

$2g = 4$

$g = 2$