Vijay is a woodworker, and he has a backlog of orders for his two most popular items: floating shelves and cutting boards. It takes him 3 hours to make a floating shelf and 2 hours to make a cutting board. This week, he wants to work at most 40 hours on these items.
Which pairs (f,c) represent possible numbers of floating shelves and cutting boards Vijay could make this week?
(8,8), (5,12) (3,16) (0,20)
The total number of hours Vijay can work this week is at most 40 hours.
Let's represent the number of floating shelves as f and the number of cutting boards as c.
The time taken to make f floating shelves is 3f hours.
The time taken to make c cutting boards is 2c hours.
Given:
3f + 2c ≤ 40
Now let's plug in the possible pairs and see if they satisfy the inequality:
(8,8):
3(8) + 2(8) = 24 + 16 = 40
This pair satisfies the inequality.
(5,12):
3(5) + 2(12) = 15 + 24 = 39
This pair also satisfies the inequality.
(3,16):
3(3) + 2(16) = 9 + 32 = 41
This pair does not satisfy the inequality.
(0,20):
3(0) + 2(20) = 0 + 40 = 40
This pair satisfies the inequality.
Therefore, the possible pairs that represent the numbers of floating shelves and cutting boards Vijay could make this week are (8,8), (5,12), and (0,20).