The Sugar Sweet Company will choose from two companies to transport its sugar to market. The first company charges $4995 to rent trucks plus an additional fee of $200.75 for each ton of sugar. The second company charges $6500 to rent trucks plus an additional fee of $125.50 for each ton of sugar.

To determine which company is more cost-effective for the Sugar Sweet Company, let's define the costs for both companies based on the number of tons of sugar transported.

Let:
- $ x $ represent the number of tons of sugar transported.

### First company:
- Fixed cost: $4995
- Cost per ton: $200.75

So, the total cost for the first company is:
\[
C_1 = 4995 + 200.75x
\]

### Second company:
- Fixed cost: $6500
- Cost per ton: $125.50

So, the total cost for the second company is:
\[
C_2 = 6500 + 125.50x
\]

Now, if you want to find out at what number of tons one company becomes more cost-effective than the other, you can set the two cost equations equal to find the breakeven point.

\[
4995 + 200.75x = 6500 + 125.50x
\]

Now, let's solve for $ x $:

\[
200.75x - 125.50x = 6500 - 4995
\]
\[
75.25x = 1505
\]
\[
x = \frac{1505}{75.25} \approx 20
\]

So, at about 20 tons of sugar, the cost of both companies will be the same.

### Conclusion:
- If the Sugar Sweet Company transports **less than 20 tons**, the second company (which charges $6500 + $125.50 per ton) will be cheaper.
- If the company transports **more than 20 tons**, the first company (which charges $4995 + $200.75 per ton) will be more cost-effective.

Would you like more details or have any questions about this solution?

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Here are 5 relative questions to explore further:
1. How much would each company charge to transport 10 tons of sugar?
2. How much would each company charge to transport 30 tons of sugar?
3. What would be the savings if the Sugar Sweet Company transported 25 tons of sugar with the cheaper option?
4. How does changing the fixed cost affect the breakeven point?
5. What if the cost per ton for the first company changed to $180.00 per ton?

**Tip:** When comparing costs, identifying the breakeven point helps you decide based on the quantity involved.

This problem explores a breakeven analysis for the Sugar Sweet Company, comparing two transport companies with different fixed costs and costs per ton of sugar. Learn how to determine which company is more cost-effective based on the number of tons of sugar transported. Suitable for students in Grades 8-10.

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