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?

(a)

(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:

From the second, we have:

Solving (a): The equations

This has been solved above.

The equations are:

Solving (b):

--- (1)

--- (2)

Multiply (2) by 2

* 2

----- (3)

Subtract (3) from (1)

Substitute 0.75 for b in (2)

Collect Like Terms

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0

linear pair postulates