Geometry 1 QUESTION help?

Question

Tallahassee was established as the capitol of Florida because it was between Pensacola and St. Augustine. The distance from Pensacola to Tallahassee can be represented as (3x + 40) miles. The distance from Tallahassee to St. Augustine can be represented as (4x + 5) miles. The distance from Pensacola to St. Augustine is 395 miles. Is Tallahassee the midpoint of Pensacola and St. Augustine? Show your work to support your conclusion.

Answer 1

The distance from Pensacola to Tallahassee (3x+40) plus (+) the distance from Tallahassee to St. Augustine (4x+5) equals (=) the distance from Pensacola to St. Augustine (395).  

(3x+40)+(4x+5)=395

Combine like terms

7x+45=395

Subtract 45 from both sides

7x=350

Divide both sides by 7

x=50

Now, you can figure out that the distance from Pensacola to Tallahassee is 3*50+40 miles by plugging in 50 for x.

3*50+40=150+40=190

Find the distance from Tallahassee to St. Augustine either by taking the total distance minus 190 or by plugging in 50 for x.  I'll just subtract 395 - 190 = 205

Since one distance is 190 and the other distance is 205, it's not the midpoint.  But, it's really close :)

_/

Answer 2

1) Write it out

3x+40+4x=5= 395

2)Combine like terms

7x+45=395

3) Simplify

7x= 350

4) Solution

x= 50

Now to figure out whether it is the middle point you have to plug in x in each equation.

3(50) + 40 = 190

4(50) + 5 = 205

No it is not the middle point.