The Sugar Sweet Company will choose from two companies to transport its sugar to market. The first company charges $7143 to rent trucks plus an additional fee of $225.75 for each ton of sugar. The second company charges $7500 to rent trucks plus an additional fee of $200.25 for each ton of sugar.For what amount of sugar do the two companies charge the same?tonsWhat is the cost when the two companies charge the same?$
Question
The Sugar Sweet Company will choose from two companies to transport its sugar to market. The first company charges 225.75 for each ton of sugar. The second company charges 200.25 for each ton of sugar.For what amount of sugar do the two companies charge the same?tonsWhat is the cost when the two companies charge the same?$
Solution
To find out the amount of sugar for which both companies charge the same, we need to set up an equation where the total cost of the first company equals the total cost of the second company.
Let's denote the amount of sugar as x (in tons).
The total cost for the first company is 225.75x. The total cost for the second company is 200.25x.
Setting these two equal to each other gives us the equation:
7143 + 225.75x = 7500 + 200.25x
To solve for x, we first subtract 200.25x from both sides:
7143 + 25.5x = 7500
Then, subtract 7143 from both sides:
25.5x = 357
Finally, divide both sides by 25.5 to solve for x:
x = 357 / 25.5 = 14 tons
So, the two companies charge the same for 14 tons of sugar.
To find the cost when the two companies charge the same, we can substitute x = 14 into the equation of either company's total cost. Let's use the first company's equation:
Cost = 7143 + 225.75 * 14 = $10166.5
So, the cost when the two companies charge the same is $10166.5.
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