Tallahassee was established as the capitol of Florida because it was between Pensacola and St. Augustine. The distance from Pensacola to Tallahassee is 190 miles. The distance from Tallahassee to St. Augustine can be represented as (5x + 5) miles. The distance from Pensacola to St. Augustine can be represented as (9x + 35) miles. Is Tallahassee the midpoint of Pensacola and St. Augustine? Show your work to support your conclusion.
2007-08-30 17:03:53 · 4 answers · asked by xlhollisterboi 1 in Science & Mathematics ➔ Mathematics
There are two good ways to do this, see which one makes more sense to you:
1. The total distance from Pensacola to St. Augustine is
190 + (5x + 5) = (9x + 35)
<=> 5x + 195 = 9x + 35
<=> 4x = 160
<=> x = 40.
Then the distance from Tallahassee to St Augustine is 5x+5 = 205 miles, which is not the same as the distance from Tallahassee to Pensacola (190 miles), so it is not the midpoint.
2. If it is the midpoint, then the distance from Pensacola to St Augustine must be twice the distance from Pensacola to Tallahassee, so
9x + 35 = 380
<=> x = 115/3 = 38.3 approx.
Also, the distance from Pensacola to Tallahassee must be the same as the distance from St Augustine to Tallahassee, so
190 = 5x + 5
<=> x = 185 / 5 = 37.
Since we get different answers for x, Tallahassee cannot be the midpoint of Pensacola and St. Augustine.
Personally I prefer the first method above, because it lets you see easily how close it is to being the midpoint (190 miles in one direction, 205 miles in the other, so it's only 7.5 miles off being the midpoint, which is pretty close really when you're talking about cities.)
2007-08-30 17:17:11 · answer #1 · answered by Scarlet Manuka 7 · 0⤊ 0⤋
t to p = 190
t to sta = 5x +5
p to sta = 9x +35
so t to p = 9x +35 -(5x +5)
190 = 9x -5x +35 -5
190 = 4x +30
160 = 4x
x = 40
so tallahasee to st augustine = 5x +5 = 5 * 40 +5 = 205 miles
tallahasee to pensacola = 190 miles
pensacola to st augustine - 9*40 + 35 = 395 miles
midpoint should be 395/2 = 1971/2 miles
so its NOT the midpoint but out by 7.5 miles
2007-08-31 00:28:42 · answer #2 · answered by mark 6 · 0⤊ 0⤋
TP = 190
ST = 5x + 5
SP = 9x + 35
=> ST + TP = 9x + 35
=> 5x + 5 + 190 = 9x + 35
=> 4x = 160 => x = 40 and
TP = 190,
ST = 5x + 5 = 5(40) + 5 = 205
SP = 9x + 35 = 9(40) + 35 = 395
As ST and TP are different,
T is not the midpoint of SP
2007-08-31 00:12:49 · answer #3 · answered by sv 7 · 0⤊ 0⤋
5x + 5 + 190 = 9x +35
160 = 4x
40 = x
190 = 5(40) + 5
190 = 205
False
It is not the midpoint.
2007-08-31 00:14:39 · answer #4 · answered by monomono4 2 · 0⤊ 0⤋