Question

Joelle plans to sell two types of balloons at her charity event: 171717‑inch latex balloons that require 222 cubic feet (\text{ft}^3)(ft 3 )left parenthesis, f, t, start superscript, 3, end superscript, right parenthesis of helium and 181818‑inch mylar balloons that require only 0.5 \,\text{ft}^30.5ft 3 0, point, 5, space, f, t, start superscript, 3, end superscript. She only has access to 1{,}000 \,\text{ft}^31,000ft 3 1, comma, 000, space, f, t, start superscript, 3, end superscript of helium, 15\%15%15, percent of which will be unused due to pressure loss in the tanks. She wants to have at least 500500500 balloons for sale in total. For the number of latex balloons, LLL, and number of mylar balloons, MMM, which of the following systems of inequalities best represents this situation? Choose 1 answer:

Answer 1

The system of inequalities would be:

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

The first inequality deals with the total number of balloons. She wants the total to be at least 500, so add the variables and set it greater than or equal to 500.

The second inequality deals with the helium. 2L comes from each latex balloon using 2 ft^3 of helium. 0.5M comes from each Mylar balloon using 0.5 ft^3. Together they can use no more than 85% of the 1000 ft^3 tank; 85% = 0.85; 0.85×1000=850. "No more than" tells us it must be less than or equal to.