Question

A carpenter has at most $250 to spend on lumber. The inequality 8x+12y≤250 represents the numbers x of 2-by-8 boards and the numbers y of 4-by-4 boards the carpenter can buy. Can the carpenter buy twelve 2-by-8 boards and fourteen 4-by-4 boards?

Answer 1

The carpenter cannot buy twelve 2-by-8 boards and fourteen 4-by-4 boards within the $250 budget, as the total cost would be $264, exceeding the budget.

Step-by-step explanation:

A carpenter has at most $250 to spend on lumber. The inequality 8x + 12y ≤ 250 represents the numbers x of 2-by-8 boards and the number y of 4-by-4 boards the carpenter can buy. To determine if the carpenter can buy twelve 2-by-8 boards and fourteen 4-by-4 boards, we substitute x with 12 and y with 14 in the inequality:

8(12) + 12(14) ≤ 250

Simplify the equation:

96 + 168 ≤ 250

264 ≤ 250

Since 264 is greater than 250, the carpenter cannot buy twelve 2-by-8 boards and fourteen 4-by-4 boards without exceeding the budget.

Answer 2

No, (12, 14) this is not a solution of the inequality

Step-by-step explanation:

(x, y)

x = 12 2-by-8 boards

y = 14 4-by-4 boards

(12, 14)

8x + 12y <= $250

This means that a 2-by-8 board cost $8 each, while a 4-by-4 board cost $12 each.

8(12) + 12(14) <= 250

96 + 168 <= 250

264 <= 250

264 is not less than or equal to 250