Manufacturing, no solid numbers except the sum.

Question

A manufacturer produces three models of DVD Players in a year. Four times as many of model A are produced as model C, and 7000 more of model B than C. If the total production for the year is 97 000 units, how many of each are produced?

Answer 1

Hi Ryan,

 

Let's begin by representing the number of production units for each model in terms of the number of production units for model "C":

    x = # of model "C" units

    4x = # of model "A" units (4 times # of model "C" units)

    x + 7,000 = # of model "B" units (7000 more than model "C" units)

 

Next, let's write an equation to express the total number of production units for all three models and then solve it for our unknowns:

    x + 4x + x + 7,000 = 97,000

    6x + 7,000 = 97,000

    6x = 97,000 - 7,000

    6x = 90,000

    x = 90,000/6

    x = 15,000 model "C" units

    4x = 4(15,000)

    4x = 60,000 model "A" units

    x + 7,000 = 15,000 + 7,000

    x + 7,000 = 22,000 model "B" units

 

We can check our answers by making sure that their sum is equal to the given total production units for all three models:

    15,000 + 60,000 + 22,000 = 97,000

    75,000 + 22,000 = 97,000

    97,000 = 97,000 (sum = total)

 

Since the sum of the production units for all three models is equal to given total production units, we are confident that our answers are correct.

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan (Romans 5:8)