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

(a)

`3b + 4g =10.25`

`2b + 2g = 5.50`

(b)

1 pound of banana = $0.75

1 pound of grape = $2.00

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`