Question

Joelle plans to sell two types of balloons at her charity event: 17-inch latex balloons that require 2 cubic feet (ft^3) of helium and 18-inch mylar balloons that require only 0.5 ft^3. She only has access to 1,000 ft^3 of helium, 15% of which will be unused due to pressure loss in the tanks. She wants to have at least 500 balloons for sale in total. For the number of latex balloons, L, and number of mylar balloon, M, which of the following systems of inequalities best represents this situation?

A. 0.5L + 2M ≤ 850
L + M ≥ 1,000

B. 2L - 0.5M ≤ 1,000
L - M ≥ 500

C. 0.5L - 2M ≤ 850
L - M ≥ 500

D. 2L + 0.5M ≤ 850
L + M ≥ 500

Answer 1

L+M >= 500 (greater than or equal to)
2L + 0.5M <= 850 (less than or equal to)

Answer 2

The correct option is D.

Explanation:

Let L be the number of latex balloons and M be the number of mylar balloon, M.

It is given that 17-inch latex balloons that require 2 cubic feet (ft^3) of helium and 18-inch mylar balloons that require only 0.5 ft^3.

Total amount of helium is

`T=2L+0.5M`

She only has access to 1,000 ft^3 of helium, 15% of which will be unused due to pressure loss in the tanks.

`1000(1-(15)/(100))=850`

`2L+0.5M\leq 850`

Therefore the

It is given that Joelle wants to have at least 500 balloons for sale in total.

`L+M\geq 500`

The system of inequalities is

`2L+0.5M\leq 850`

`L+M\geq 500`

Therefore the correct option is D.