I have been going through the Algebra lessons, and I came upon another challenge question that is confusing me. In 105, #77, I cannot figure out how to set up the problem with Jupiter and Saturn appearing at the same time. I looked at the answer and I know that 60 is the Least Common Denominator of 12 and 30, but I don't understand how to get 1/60 out of 1/12 and 1/30 (once every 12 years and once every 30 years). Maddie (Sheri's daughter)
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Problems with rational equationsPrenctice Hall Classics Algebra 1
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Maddie,
I will take a look at this when I get a chance and get back to you. Meanwhile, don't let it hold you up. Keep going with your studies.
Mrs. DavisCindy Davis
Science and Math teacher at Highlands Latin School  Indianapolis
ds24 college graduate: working, reading, writing
ds23 college graduate: 1st year med school
dd21 college junior: Nursing

Hi Maddie,
#76, #77, and #78 are simply Least Common Multiple problems, because you are looking for integer multiples of laps or orbits, where the runners or planets are passing the same place.
I think that is easiest to see in #76. If runner A crosses the start line every 6 minutes, and runner B crosses the start line every 8 minutes, they will cross the start line *together* again at the LCM of 6 and 8, which is 2x3x4 = 24 minutes.
Similarly for #77, Earth crosses the "start" line every year, Jupiter every 12 years, and Saturn every 30 years, so they will cross the "start" line together at the LCM of 1, 12, and 30, which is 2x2x3x5 = 60 years.
See if you can figure out the answer to #78.
I will check back to see if you got it correct.Last edited by Cindy in Indy; 03082019, 10:09 AM.Cindy Davis
Science and Math teacher at Highlands Latin School  Indianapolis
ds24 college graduate: working, reading, writing
ds23 college graduate: 1st year med school
dd21 college junior: Nursing
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That's correct! 420 is the LCM of 1,12,30, 84: 2x2x3x5x7=420.
Congratulations, and keep up the good work!Cindy Davis
Science and Math teacher at Highlands Latin School  Indianapolis
ds24 college graduate: working, reading, writing
ds23 college graduate: 1st year med school
dd21 college junior: Nursing
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