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Question

A car manufacturing company can produce a car for $3000 and a truck for $5000. Suppose C cars and T trucks are sold to the dealer at mark ups, respectively of 20 and 30 percent. If the company made a profectvof $27million on sales of $137million in one particular year, how many cars and trucks were sold by the company in that year

Answer 1

Profit is 27,000,000 out of 137,000,000

Profit = revenue - cost

That means cost was 110,000,000

 

cost :  3000C + 5000T = 110,000,000

 

revenue: 1.2(3000)C + 1.3(5000)T = 137,000,000

              3600C+ 6500T = 137,000,000

 

We have two equations.

Let's smplify by dividing everything by1000:

 

3C + 5T = 110,000        {equation1}

3.6C + 6.5T = 137,000  {equation 2}

 

multiply equation 1 by -1.2 and add equations

 

-3.6C  - 6T = -132,000

 3.6C + 6.5T = 137,000

------------------------------

        0.5T = 5,000

         T = 10,000 trucks

 

3C + 5T = 110,000

3C + 50,000 = 110,000

3C = 60,000

C = 20,000 cars

 

They sold 20,000 cars and 10,000 trucks

 

Check:

cost = $110,000,000

3000(20,000) + 5000(10,000)

= 60,000,000 + 50,000,000

= 110,000,000

 

Revenue = $137,000,000

3600(20,000) + 6500(10,000)

= 72,000,000 + 65,000,000

= $137,000,000

 

Profit = revenue- cost = $27,000,000