Word problem - Algebra

Question

A machine requires three hours to make product A and nine hours to make product B. Last month the machine operated for 918 hours producing a total of 132 units. How many units of product A and product B were produced?

Answer 1

At onset, we will have two equations, thus we will need to equations. 

 

Machine A takes 3 hours to produce a product, while Machine B takes 9 hours to produce a product. 

 

The sum of the product of the time it takes each individual machine and the amount of products they produce should be equal to the overall time the machine was ran for the month. 

 

The two equations we get are:

 

a + b = 132, which is the number of units total. The sum of how many units Machine A can produce and Machine B has to total 132, which is stipulated by the problem.

 

The constraint equation is: 

 

3a + 9b = 918, which is the sum product of the amount of each individual machine output and time it takes will equal the overall total time the machines ran. 

 

We solve for b in the first equation and place the result in the second. We get: 

 

3a + 9(132-a) = 918 

3a + 1188 -9a = 918 

 

-3a = -280 

 

a =90, thus b = 42, this is the number of units each machine produced.