Question

Merv only has $18 to spend at the store and needs to by x number of apples and y number of oranges for snacks at the baseball game. This is represented by the inequality 3x+2y≤18 as shown on the graph. Which one of the three points shown is a viable solution and explain why the other two are not viable. (Requires 3 sentences; one about each point explaining why it is a solution or not).
Points given: (4,5), (4,3), and (1.5, 2) (4,3) is correct

Answer 1

The point (4, 5) is not a viable solution because substituting x = 4 and y = 5 into the inequality gives 3(4) + 2(5) = 12 + 10 = 22, which exceeds the budget of $18. The point (1.5, 2) is also not viable since plugging in x = 1.5 and y = 2 results in 3(1.5) + 2(2) = 4.5 + 4 = 8.5; while this is under the budget, it is not a maximum utilization scenario relative to other points. The point (4, 3) is a viable solution because substituting x = 4 and y = 3 gives 3(4) + 2(3) = 12 + 6 = 18, which exactly meets the budget constraint.