SOLUTION: it takes Mars 1.88 years to travel around the sun.It takes Mercury 0.24 years to orbit the sun. If the planets are in a straight line with the sun now, how long will it be before t

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Question 87072: it takes Mars 1.88 years to travel around the sun.It takes Mercury 0.24 years to orbit the sun. If the planets are in a straight line with the sun now, how long will it be before this is the case again? The answer must be accurate to the nearest hundredth of a year.
Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
it takes Mars 1.88 years to travel around the sun.It takes Mercury 0.24 years to orbit the sun. If the planets are in a straight line with the sun now, how long will it be before this is the case again? The answer must be accurate to the nearest hundredth of a year.
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You need the least common multiple of 1.88 and 0.24
In 282 years mars will have orbited 150 times
In 282 years mercury will have orbited 1175 times.
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Cheers,
Stan H.

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

it takes Mars 1.88 years to travel around the sun.It takes Mercury 0.24 years
to orbit the sun. If the planets are in a straight line with the sun now, how
long will it be before this is the case again? The answer must be accurate to
the nearest hundredth of a year.

We must find the smallest positive integer N 
such that when we multiply both 1.88 and .24 by N 
we get a positive integer, that is

1.88N = P , whener P is a positive integer
 and

0.24N = Q , whener Q is also a positive integer

Multiply both equations by 100 to remove decimals:

188N = 100P

24N = 100Q

Solve each for N

N = 100P%2F188

N = 25P%2F47

N = 100Q%2F24

N = 25Q%2F6

So we have

25P%2F47 = 25Q%2F6

Divide both sides by 25

P%2F47 = Q%2F6

Cross multiply:

6P = 47Q

Divide both sides by 6Q

%286P%29%2F%286Q%29 = %2847Q%29%2F%286Q%29 

P%2FQ = 47%2F6

The smallest positive integer values of P and Q
which make that equation true are P = 47 and
Q = 6.

Substitute 47 for P in

1.88N = P

1.88N = 47

N = 47%2F1.88

N = 25

As a check:

Substitute 6 for Q in

0.24N = Q

0.24N = 6

N = 6%2F0.24

N = 25

So the answer is 25 years. That's the next time when 
both planets will have each completed a whole number 
of revolutions.

Edwin