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 sell?

Answer 1

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.

Answer 2

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

• Let x = number of baseball racks sold

• Let y = number of karate-belt racks sold

Based on the information given, the equation to solve the question will be:

x = 6y ....... I

3x + 5y = 46000 ....... equation ii

We'll then substitute equation i into equation ii and this will be:

3x + 5y = 46000

3(6y) + 5y = 46000

18y + 5y = 46000

23y = 46000

y = 46000/23

y = 2000

Therefore, x will be:

x = 6y

x = 6 × 2000 = 12000.

Therefore, they should sell 2000 karate-belt racks and 12000 baseball racks.

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