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## solving application linear equations

if planet one is 29.3 miles farther from the sun than planet two, then planet three is 25.4 miles farther from the sun than planet one. When the total of distances for these three planets from the sun is 192.0 miles, how far away from the sun is planet two?
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# 4 Answers

For lack of a drawing tool, the planets look like this:

SUN <-- D2 --> P2 <--29.3 --> P1 <-- 25.4 --> P3

where the P's are the planets and the # are the distances between as given.

We need to find D2, distance of P2 from the sun.

The sum of the distances of the planets fro the Sun is information given.

D2 = distance of P2 from Sun

D1 = distance of P1 from Sun = D2 + 29.3

D3 = distance of P3 from the Sun = D2 + 29.3 + 25.4

D1 + D2 + D3 = 'total of distances for these three planets from the sun' = 192.0

D1 + D2 + D3 = (D2 +29.3) +(D2) + (D2 + 29.3 + 25.4) =192.0

3*D2 + (29.3 + 29.3 + 25.4) =192

3*D2 + 84.0 = 192

3*D  = 192 - 84

D2 = 108/3

D2 = 36 miles  DISTANCE OF PLANET 2 FROM THE SUN.

BruceS

let x be the distance planet 2 is from the sun
let x+29.3 be the distance planet 1 is from the sun
let x+29.3+25.4 be the distance planet 3 is from the sun
add the distances
x+x+29.3+x+29.3+25.4=192
3x+84=192
3x=108
x=36 miles
Let x = the distance from the sun to planet 2.

x + 29.3 = the distance from the sun to planet 1.

(x + 29.3) + 25.4 = the distance from the sun to planet 3.

Now, find the sum of the distances:
x + x + 29.3 + x + 29.3 + 25.4 = 192

Combine like terms:
3x + 84 = 192

Subtract 84 from both sides:
3x = 108
x = 36

Planet 2 is 36 miles from the sun.
x = distance to planet 2
x + 29.3 = distance to planet 1

x + 29.3 + 25.4 = distance to planet 3

(x) + (x + 29.3) + (x + 29.3 + 25.4) = 192

3x + 58.6 + 25.4 = 192

3x + 84 = 192

3x = 192-84

3x = 108

x = 36 miles (planet 2)

36+29.3 = 65.3 for planet 1

36 + 29.3 + 25.4 = 65.3 + 25.4 = 90.7 for planet 3

36
65.3
90.7
-----
192.0 It worked.