A system of inequalities to model the scenario is x ≥ 3 and 12x + 7y ≤ 63.
A graph of the system of inequalities is shown below.
The solution set lies within the region that is shaded purple with a constraint of y ≥ 0.
In order to write a system of inequalities to describe this situation, we would assign variables to the amount of live bait and the amount of natural bait respectively, and then translate the word problem into a linear inequality as follows:
- Let the variable x represent the amount of live bait.
- Let the variable y represent the amount of natural bait.
Based on the information provided above, the bait shop sells live bait for $12 a pound and natural bait for $7 a pound, but John only has a budget of $63 and would like to get at least 3 pounds of live bait.
In this context, a system of inequalities that models this scenario can be written as follows;
x ≥ 3
12x + 7y ≤ 63
Furthermore, a graph of the system of inequalities is shown below and the solution set lies within the region that is shaded purple with a constraint of y ≥ 0. Hence, a possible solution is (4, 1), which means 4 pounds of live bait and a pound of natural bait.