Question

The Sugar Sweet Company will choose from two companies to transport its sugar to market. The first company charges $2804 to rent trucks plus an additional

fee of $100.50 for each ton of sugar. The second company does not charge to rent trucks but charges $275.75 for each ton of sugar.

For what amount of sugar do the two companies charge
the same?

What is the cost when the two companies charge the
same?

Answer 1

• 16 tons

• $4412

Explanation:

We can rewrite the situation using cost equations for the two companies

If c1 and c2 represent the total costs for companies 1 and 2 respectively and w the weight of sugar transported

For the first company we have
c1 = 2804 + 100.50w

For the second company
c2 = 275.75w

Costs are the same when c1 = c2

or

2804 + 100.50w = 275.75w

To Solve:

• Subtract 100.50w from both sides
  2804 + 100.50w - 100.50w = 275.75w - 100.50w
  2804 = 175.25w
  
• Switch sides
  175.25w = 2804
  
• Divide by 175.25:
  175.25w/175.25 = 2804 /175.25
  w = 16
  

At 16 tons of sugar, the costs will be the same for both companies

At this tonnage, the cost is
275.75 x 16 = $4412