The sugar sweet company will choose from two companies to transport its sugar to market. the first company charges 6597 to rent trucks plus an additional fee of $200.75 for each ton of sugar. the second company charges $7500 to rent trucks plus an additional fee of $125.50 for each ton of sugar. for what amount of sugar do the companies charge the same? what is the cost when two companies charge the same?

The cost when two companies charge the same is $ 9006

Solution:

Let "x" be the tons of sugar

The first company charges 6597 to rent trucks plus an additional fee of $200.75 for each ton of sugar

Therefore,

Amount for first company: 6597 + 200.75(tons of suagr)

Amount for first company: 6597 + 200.75x --------- eqn 1

The second company charges $7500 to rent trucks plus an additional fee of $125.50 for each ton of sugar

Therefore,

Amount for second company: 7500 + 125.50(tons of sugar)

Amount for second company: 7500 + 125.50x --------- eqn 2

For what amount of sugar do the companies charge the same?

For both the companies to charge the same, eqn 1 must be equal to eqn 2

6597 + 200.75x = 7500 + 125.50x

200.75x - 125.50x = 7500 - 6597

75.25x = 903

x = 12

Thus for 12 tons of sugar, both the companies charge the same

What is the cost when two companies charge the same?

Substitute x = 12 in any one of equations

Let us substitute x = 12 in eqn 1

Thus the cost when two companies charge the same is $ 9006