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 sell?

Let the number of baseball racks sold be x.

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

a)

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

b)

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

c)

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