It takes your company 6 labour hours to manufacture a simple hot tub and 9 labour hours to manufacture a deluxe hot tub. Last week your company used a total of 795 labor hours to manufacture a total of 105 hot tubs. How many of each type of hot tub did you manufacture?
A) Simple 40, Deluxe 65
B) Simple 55, Deluxe 50
C) Simple 75, Deluxe 30
D) Simple 50, Deluxe 55
E) Simple 65, Deluxe 50

Question

Quizplus · Accepted Answer

Let x be the number of simple hot tubs and y be the number of deluxe hot tubs.

From the problem, we know that:

- 6x + 9y = 795 (total labor hours used) 
- x + y = 105 (total number of hot tubs manufactured)

We can simplify the first equation by dividing both sides by 3:

- 2x + 3y = 265

We can then multiply the second equation by 2:

- 2x + 2y = 210

Now we can subtract the second equation from the first equation to eliminate x:

- 2x + 3y = 265 
- (2x + 2y = 210) 
------------------------
- y = 55

We can substitute y = 55 into the second equation to solve for x:

- x + y = 105 
- x + 55 = 105 
- x = 50

Therefore, the company manufactured 50 simple hot tubs and 55 deluxe hot tubs.

The answer is D.

It Takes Your Company 6 Labour Hours to Manufacture a Simple