Question

Iced tea, x, costs $4 per gallon and lemonade, y, costs $6 per gallon. You need to purchase at least 9 gallons of drinks for a neighborhood picnic, but have at most $55 to spend. Model the scenario with a system of inequalities. Which of the following options represents a possible solution to the system of inequalities?

Answer 1

The answer is 10,1

The explanation is below. The graph is correct and the point 10,1 is in the shaded area that is covered by both equations.

Answer 2

The system of inequalities is equal to

`x+y\geq 9`

`4x+6y\leq 55`

The graph in the attached figure

Explanation:

Let

x------> the number of gallons of iced tea

y-----> the number of gallons of lemonade

we know that

`x+y\geq 9` -----> inequality A

`4x+6y\leq 55` -----> inequality B

using a graphing tool

the solution is the shaded area

see the graph in the attached figure