Question 1203161: The total number of known moons around Saturn, Uranus, and Neptune is 43. The total number of moons around Saturn and Neptune is 9 more than the number of moons around Uranus. Saturn has 2 moons more than twice the number of moons around Neptune. Find the number of moons each planet has.
Found 2 solutions by ikleyn, Alan3354:
Answer by ikleyn(52894)   (Show Source):
You can put this solution on YOUR website! .
The total number of known moons around Saturn, Uranus, and Neptune is 43.
The total number of moons around Saturn and Neptune is 9 more
than the number of moons around Uranus.
Saturn has 2 moons more than twice the number of moons around Neptune.
Find the number of moons each planet has.
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Let N be the number of moons around Neptune.
Then the number of moons around Saturn is 2N+2, according to the problem.
The number of moons around Uranus is ((2N+2) + N - 9) = 3N-7.
Next, we have this equation for the total number of moons around the three planets
N + (2N+2) + (3N-7) = 43.
Simplify and find N
6N - 5 = 43
6N = 43 + 5 = 48
N = 48/6 = 8.
ANSWER. There are 8 moons around Neptune;
2*8+2 = 18 moons around Saturn,
and 3*8-7 = 17 moons around Uranus.
CHECK. 8 + 18 + 17 = 43 moons, total. ! correct !
Solved.
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! The total number of known moons around Saturn, Uranus, and Neptune is 43. The total number of moons around Saturn and Neptune is 9 more than the number of moons around Uranus. Saturn has 2 moons more than twice the number of moons around Neptune. Find the number of moons each planet has.
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S + U + N = 43
S + N = U + 9
S = 2N + 2
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Sub for S:
2N+2 + U + N = 43 ---> 3N + U = 41
2N+2 + N = U+9 ------> 3N - U = 7
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3N + U = 41
3N - U = 7
------------------------- Add
6N = 48
N = 8
Etc.
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