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)

Answer 1

The point (4,5) is not a viable solution because it results in \(3(4) + 2(5) = 12 + 10 = 22\), which exceeds the budget of $18, violating the inequality. The point (4,3) is also not viable, as it leads to \(3(4) + 2(3) = 12 + 6 = 18\), which meets the budget but does not satisfy the inequality since it must be less than or equal to 18. Conversely, the point (1.5, 2) is a viable solution because \(3(1.5) + 2(2) = 4.5 + 4 = 8.5\), which is within the budget and satisfies the inequality \(3x + 2y \leq 18\).