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satela [25.4K]
4 years ago
11

HomePride manufactures solid oak racks for displaying baseball equipment and karate belts. They usually sell six times as many b

aseball 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?
Mathematics
1 answer:
kramer4 years ago
5 0
Let the number of baseball racks sold be x. 
<span>Let the number of karate-belt racks sold be y. </span>

<span>a) </span>

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

<span>Net profit from baseball racks </span>
<span>= $3x </span>

<span>Net profit from karate-belt racks </span>
<span>= $5y </span>

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

<span>b) </span>

<span>x = 6y --- (1) </span>
<span>3x + 5y = 46000 --- (2) </span>

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

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

<span>c) </span>

<span>They should sell 12000 baseball racks and 2000 karate-belt racks.</span>
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