Word problems involving percents

Question

I need help solving this problem. I'm mostly just not sure how to lay it out into an equation.

Mark works strictly on commission of his gross sales from selling two different products for his company. Last? month, his gross sales were ?$86000. If he earns 5?% commission on product A and 3?% commission on product? B, what were his gross sales for each product if he earned ?$3780 in total? commission?

Answer 1

 

Let a = sales from product A

Let b = sales from product B

 

Since the total commission was 3780,

 

            .05a + .03b = 3780       (Equation 1) ... 5%(a) = .05a ... 3%(b) = .03b

 

                 a + b = 86,000         (Equation 2) ... sum of the sales of the 2 products is the gross sales

 

Remove decimals by multiplying equation 1 by 100

 

             5a + 3b = 378,000

 

Solve using elimination method.  Multiply equation 2 by (-3), add the resulting 2 equations.

 

            5a + 3b = 378,000

           -3a - 3b = -258,000

          _________________

            2a         = 120,000

              a = 60,000

 

Since a + b = 86,000,  b = 86,000 - 60,000 = 26,000

 

So the gross sales were 60,000 for product A and 26,000 for product B