College algebra Module 1 section 2

Question

Mark works on commission of his gross sales from selling two different products for his company. Last month his gross sales were $93,000. If he earns 6% commission on product A and 5% commission on product B, what were his gross sales for each product if he earned $5300 in total commission?

Answer 1

Let A = gross sales amount for PRODUCT A

Let B = gross sales amount for PRODUCT B

A + B = 93,000 Gross Sales Amount

.06A + .05B = 5,300 Total Commission

6A + 5B = 530,000 Multiply 2nd equation by 100 to eliminate decimals. Not required.

A = 93,000 - B Solving for A in 1st equation.

6(93,000 - B) + 5B = 530,000 Substituting A into 6A + 5B = 530,000

558,000 - 6B + 5B = 530,000 Multiplying 6 times 93,000 and - B.

558,000 - B = 530,000 Combining B's

-558,000 + B = - 530,000 Multiplying entire equation by -1

B = 558,000 - 530,000 Adding 558,000 to both sides of the equation.

B = 28,000

GROSS SALES OF PRODUCT B = $28,000

USE 6A + 5B = 530,000 TO SOLVE FOR A

6A + 5B = 530,000

6A + 5(28,000) = 530,000 Substituting $28,000 for B.

6A + 140,000 = 530,000

6A = 530,000 - 140,000 Subtracting 140,000 from both sides of the equation.

6A = 390,000

A = 390,000/6 Dividing both sides by 6

A = 65,000

GROSS SALES OF PRODUCT A = $65,000

CHECKING

DOES A + B = 93,000 ?

$65,000 + $28,000 = 93,000 YES!

DOES 6A + 5B = 530,000 ?

6A + 5B = 6($65,000) + 5($28,000)

= $390,000 + $140,000

= $530,000 YES!

HOPE THIS HELPS YOU BRANDON M.