Question

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?

Answer 1

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

$\rightarrow 6597 + 200.75x = 6597 + 200.75(12)\\\\\rightarrow 6597 + 2409 = 9006$

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