The Sugar Sweet Company will choose from two companies to transport its sugar to market. The first company charges $6500 to rent trucks plus an additional fee of $125.50 for each ton of sugar. The second company charges $5897 to rent trucks plus an additional fee of $175.75 for each ton of sugar.

Question

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

Let x be the amount of sugar in tons.

For the first company:
Cost = $6500 + $125.50x

For the second company:
Cost = $5897 + $175.75x

Setting these two costs equal to each other:
$6500 + $125.50x = $5897 + $175.75x
$602.75 = $50.25x
x = 12

Therefore, the two companies charge the same amount for 12 tons of sugar.

Plugging in x=12 into either cost equation:
Cost = $6500 + $125.50(12) = $6500 + $1506 = $8006
So, the cost when the two companies charge the same is $8006 for 12 tons of sugar.

Answer 2

You sure?

Answer 3

Apologies for the miscalculation. Let me correct that.

Setting the two costs equal to each other:
$6500 + $125.50x = $5897 + $175.75x
$6500 - $5897 = $175.75x - $125.50x
$603 = $50.25x
x = $603 / $50.25
x = 12

So, the two companies charge the same amount for 12 tons of sugar.

Plugging in x=12 into either cost equation:
Cost = $6500 + $125.50(12) = $6500 + $1506 = $8006

Therefore, the cost when the two companies charge the same is $8006 for 12 tons of sugar.