Question

Latisha wants to buy pumpkins and autumn squash for a fall display. She has a budget of no more than $117 but wants to buy more than 10 vegetables for the decorations. The pumpkins are $5.50 each and the autumn squash are $3.50 each. Part A: Write a system of linear inequalities to represent the situation. Part B: List three possible combinations of pumpkins and squash that Latisha can purchase to represent the situation. Part C: If Latisha decides she is going to use 12 pumpkins for the display, what is the maximum number of squash she can use?

Answer 1

Answer with explanation:

Total Money that Latisha has =$ 117

Number of Vegetables that latisha want to buy=More than 10 vegetables

Cost of a Pumpkin =$ 5.50

Cost of an Autumn Squash = $ 3.50

Let number of pumpkin bought=x

Number of Autumn Squash bought = y

⇒⇒ The following inequality which describes the above situation are

Part A

1.→ x+y≥ 10

2.→ 5.50 x + 3.50 y ≤ 117

Part B----(Three possible combinations of pumpkins and squash that Latisha can purchase to represent the situation.)

Taking , x as independent variable, we can find distinct y's.

x ( Pumpkin) y(Autumn squash)--An Integral value

8 20

6 24

10 17

Part C

x=12-----Number of Pumpkins

→5.50 × 12+ 3.50 y ≤117

→66 +3.50 y ≤117

→3.50 y ≤117-66

→3.50 y ≤ 51

→y <15 or y≤14

Maximum number of squash Latisha can use=14(An Integral value)