This is a "Solving Systems of equations in two variables" problem.

Question

HomePride manufactures solid oak racks for displaying baseball equipment and karate belts. They usually sell six times as many baseball racks as karate-belt racks. The net profit is $3 from each baseball rack and $5 from each karate-belt rack. If the company wants a total profit of $46,000, how many of each type of rack should they sale?

Answer 1

Let the number of baseball racks sold be x.
Let the number of karate-belt racks sold be y.



Since 6 times as many baseball racks is sold as karate-belt racks, we have:
x = 6y, which is our first equation

Net profit from baseball racks
= $3x

Net profit from karate-belt racks
= $5y

Total profit is $46000, so we have:
3x + 5y = 46000, which is our second equation



x = 6y --- (1)
3x + 5y = 46000 --- (2)

Substituting (1) into (2), we will get:
3(6y) + 5y = 46000
18y + 5y = 46000
23y = 46000
y = 46000 / 23
y = 2000

Substituting y = 2000 into (1), we will get:
x = 6(2000)
x = 12000


They should sell 12000 baseball racks and 2000 karate-belt racks.