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.