Last month. his gross sales were $85,000. If he earns 6% commission on product A and 4% commission on product B, what were his gross sales for each product if he earned $4700 in total commission

Question

i need Gross sales for product A and gross sales for product B

Answer 1

There are two variables here which often indicates a system of equations will be required to solve for the two variables. First lets define our variables. We know what needs to be represented by variables based on the question they are asking us to answer. "What were his gross sales for each product?"

Let

A = gross sales of product A in dollars

B =gross sales of product B in dollars

The first equation can be found from knowing his gross total sales were $85,000 and only two items he sells are A and B. So A + B = 85,000

The next equation is found by understanding the concept of commission. commission is a dollar amount earned based on a percentage of the sales. So if 6% commission on product A means he earns 6% of sales price of A for each product A sold, .06 A. So to find commission for product B we would use .04 B. We are told total commission earned is $4700 so .06 A + .04 B = 4700

We now have our system of equations with two variables

EQ 1: A + B = 85,000

EQ2: .06 A + .04 B = 4700

We can rewrite EQ 1 as B = 85,000 - A and then substitute that in for B in EQ2

.06 A + .04 (85,000- A) = 4700...now we solve this equation for A

.06 A +3400 - .04 A = 4700

.02 A +3400 = 4700

.02 A = 1300

A = 65000

We now plug 65,000 into A in first equation to find B

65,000 + B = 85,000

B = 20,000

Gross sales of product A were $65,000 and gross sales of product B were $20,000