Question

Part ASteve buys 2 lb of grapefruit and 3 lb of oranges for $7.20. Kennedy buys 4 lb of grapefruit and 2 lb of oranges for $8.80. Let x represent the price per pound for grapefruit, and let y represent the price per pound for oranges. Choose the system of equations that models the situation.A.2x + 3y = 7.202x + 4y = 8.80B.3x + 2y = 7.204x + 2y = 8.80C.2x + 3y = 7.204x + 2y = 8.80D.2x + 3y = 8.804x + 2y = 7.20Part BSteve buys 2 lb of grapefruit and 3 lb of oranges for $7.20. Kennedy buys 4 lb of grapefruit and 2 lb of oranges for $8.80. Let x represent the price per pound for grapefruit, and let y represent the price per pound for oranges. Use the system of equations from Part A to find the price per pound for oranges.price: $ per pound

Answer 1

PartA

If x represents the price per pound of grapefruit, and y the price per pound of orange, then, based on the given information, you have the following system of equations:

2x + 3y = 7.20 (what Steve bought)

4x + 2y = 8.80 (what Kennedy bought)

PartB

In this case, it is necessary to solve the system of equations. Proceed as follow:

Multiply the first equation of the system by -2, sum the result to the second equation of the system, and solve for y:

(2x + 3y = 7.20)(-2)

-4x - 6y = -14.40

-4x - 6y = -14.40

4x + 2y = 8.80

-4y = -5.60

y = 5.60/4

y = 1.40

Next, replace the previous value of y into any of the equations of the system and solve for x:

2x + 3y = 7.20

2x + 3(1.40) = 7.20

2x + 4.20 = 7.20

2x = 7.20 - 4.20

2x = 3.20

x = 3.20/2

x = 1.60

Hence, the price per pound for grapefruits and oranges is, respectively, $1.60 and $1.40