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?
Math help needed here!
=)
distancePensacolatoAugustine=distPT + distanceTA
395=3x+40 + 4x+5
solve for x. I get about 50. Then, see if the distance from Pensacola to Tallassee (3x_+40) is half of 395
distancePensacolatoAugustine=distPT + distanceTA
395=3x+40 + 4x+5
solve for x. I get about 50. Then, see if the distance from Pensacola to Tallassee (3x_+40) is half of 395
Yes!
we can set up the equation 3x+40+4x+5=395 and solve to get
7x+45=395
7x=350 so x=50
When we plug it in to check, we get
3(50)+40+4(50)+5=395
so the answer must be correct!
To determine if Tallahassee is the midpoint between Pensacola and St. Augustine, we need to check if the distance from Pensacola to Tallahassee (represented as 3x + 40) is half the total distance from Pensacola to St. Augustine (395 miles).
We start by setting up the equation:
3x + 40 = (395)/2
Next, we solve for x:
3x = (395/2) - 40
3x = 197.5 - 40
3x = 157.5
x ≈ 52.5
Now, we substitute this value of x back into the equation for the distance from Pensacola to Tallahassee:
3(52.5) + 40 = 157.5 + 40 = 197.5
Since the distance from Pensacola to Tallahassee is 197.5 miles, and half the total distance from Pensacola to St. Augustine (395 miles) is also 197.5 miles, we can conclude that Tallahassee is indeed the midpoint between Pensacola and St. Augustine.