Complete Question
The first company charges 6500 to rent trucks plus an additional fee of 125.50 for each ton of sugar. The second company charges 5597 to rent trucks plus an additional fee of 200.75 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:
(a)12 Tons
(b)$8,006
Explanation:
Let the number of ton of sugar at which the company charge the same=n
The first company charges 6500 to rent trucks plus an additional fee of 125.50 for each ton of sugar.
Therefore, its total charge =6500+125.50n
The second company charges 5597 to rent trucks plus an additional fee of 200.75 for each ton of sugar.
Therefore, its total charge =5597+200.75n
Since the two companies charges are the same at n tons
6500+125.50n=5597+200.75n
Collect like terms
6500-5597=200.75n-125.50n
903=75.25n
Divide both sides by 75.25 to solve for n
n=903/75.25
n=12
Therefore, at 12 tons, the two companies charges the same.
Next, we substitute n=12 into any of the equation to determine the cost when the two companies charge the same.
Using the equation 6500+125.50n
At n=12
6500+125.50(12)=$8,006
The cost when the two companies charge the same is $8,006