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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?

### 4 Answers by Expert Tutors

BRUCE S. | Learn & Master Physics & Math with Bruce SLearn & Master Physics & Math with Bruce...
4.9 4.9 (36 lesson ratings) (36)
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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

Arthur D. | Effective Mathematics TutorEffective Mathematics Tutor
4.8 4.8 (13 lesson ratings) (13)
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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
x+x+29.3+x+29.3+25.4=192
3x+84=192
3x=108
x=36 miles
Nancy K. | A-1 Experienced Resource Teacher - All Grades A-1 Experienced Resource Teacher - All G...
4.0 4.0 (1 lesson ratings) (1)
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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.
Jason S. | My goal is the success of my students. Knowledge-Patience-HonestyMy goal is the success of my students. K...
4.9 4.9 (115 lesson ratings) (115)
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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
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192.0 It worked.