Question

The Sugar Sweet Company will choose from two companies to transport its sugar to market. The first company charges $3490 to rent trucks plus an additional fee of $200.75 for each ton of sugar. The second company charges $5500 to rent trucks plus an additional fee of $100.25 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

the two companies charge the same for 20 tons of sugar.

the cost when the two companies charge the same is $7,890.

Explanation:

Let x be the amount of sugar transported in tons.

Then the total cost C1 for the first company is given by:

C1 = 3490 + 200.75x

And the total cost C2 for the second company is given by:

C2 = 5500 + 100.25x

To find the amount of sugar for which the two companies charge the same, we need to solve the equation:

C1 = C2

3490 + 200.75x = 5500 + 100.25x

Simplifying and solving for x, we get:

100.5x = 2010

x = 20

Therefore, the two companies charge the same for 20 tons of sugar.

To find the cost when the two companies charge the same, we can substitute x = 20 into either C1 or C2. For example, using C1, we get:

C1 = 3490 + 200.75(20) = 7890

Therefore, the cost when the two companies charge the same is $7,890.