Company charges 6500 to rent trucks plus additional fee of 125.50 for each ton. Second company charges 5597 to rent trucks plus an additional fee of $200.75 for each ton of sugar

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?

(a)12 Tons

(b)$8,006

Step-by-step 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

what are you trying find out?

step-by-step explanation:

tell you what. i'll find the length of the medians and you can fill in the blanks where they belong.

br

b = (2a,0)

r = (a/2,b/2) remember these things are medians. they go to the 1/2 way point of the line opposite the vertex they face.

br^2 =   (2a - a/2)^2 + (0 - b/2)^2

br^2 = (3/2 a) ^2 + b^2 / 4

br^2 = 9/4 a^2 + b^2 / 4   we need to find some relationship between a and b.

let's try ab = bc  

ab = 2a

bc = (2a - a)^2 + (b - 0)^2

bc = sqrt(a^2 + b^2)

ab = bc

2a = sqrt(a^2 + b^2) square both sides.

4a^2 = a^2 + b^2 subtract a^2 from both sides.

sqrt(3a^2) = sqrt(b^2)

sqrt(3)a = b

let's put b into br^2

br^2 = 9/4 a^2 + 3b^2 / 4

br^2 = 12 a^2 / 4

br^2 = 3a^2 

br = sqrt(3) * a

cp

c = (a,b) ; p = (a,0) this is another application of the distance formula, and it is a good one.

cp^2 = (a - a)^2 + (b - 0)^2

cp^2 = 0 + b^2

cp^2 = b^2 which you can see from the diagram. 

cp = sqrt(b^2)

cp = b but b = sqrt(3) * a 

cp = sqrt(3)*a

aq

a = (0,0)

q = (3/2) a, b/2

aq^2 = (3a/2 -0)^2 + (b/2 - 0)^2

aq^2 = 9a^2/4 + b^2/4

but b = sqrt(3) * a 

aq^2 = 9a^2 / 4 + (sqrt(3)*a)^2 /4

aq^2 = 9 a^2/ 4 + 3 a^2 / 4

aq^2 = 12 a^2/4

aq^2 = 3 a^2

aq = (sqrt  3) * a which agrees with the other two.