It takes 40 minutes to produce product A and 60 minutes to produce product B. Last week 60 hours were used in manufacturing both products. A total of 70 units were produced. Determine the number of product A and B produced.
A) Product A = 20; Product B = 50
B) Product A = 30; Product B = 40
C) Product A = 10; Product B = 60
D) Product A = 40; Product B = 30

Question

Quizplus · Accepted Answer

Let's assume that the number of product A produced is x and the number of product B produced is y.

From the problem statement, we know that:
- It takes 40 minutes to produce product A, so x units of product A will take 40x minutes.
- It takes 60 minutes to produce product B, so y units of product B will take 60y minutes.
- Last week 60 hours were used in manufacturing both products, which is a total of 60*60 = 3600 minutes.
- A total of 70 units were produced, so x + y = 70.

Combining the first two equations, we get 40x + 60y = total minutes spent on production.

We can use these equations to form a system of equations:

40x + 60y = 3600 (total minutes spent on production)
x + y = 70 (total number of units produced)

We can solve for x and y using substitution or elimination.

Using substitution:
- x = 70 - y (from the second equation)
- 40(70 - y) + 60y = 3600 (substitute x into the first equation and simplify)
- 2800 - 40y + 60y = 3600
- 20y = 800
- y = 40
- x = 70 - y = 30

Therefore, the number of product A produced is 30 and the number of product B produced is 40, which matches answer choice B.

It Takes 40 Minutes to Produce Product a and 60