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please answer this math qusetion?
one radio station brocasts a weather forcast every 18 minutes and another station brocasts a commercial every 15 minutes. If the stations brocast both a weather forecast and a commercial at noon, when is the next time tha tboth will be broadcast at the same time?
and this one,
mckenzie is making bead necklaces.He has 90 green beads and 108 blue beads. what is the greatest # of identical necklces he can make if he wants to use all of the beads?
plz help!
PROBLEM 1:
What they are asking really is what is the LCM (lowest common multiple) of 18 minutes and 15 minutes.... so you have to find the factors of both 18 and 15...
18 = 2 x 3 x 3 ... so you LCM has to be at least 2 x 3 x 3
15 = 3 x 5 .... the factor of "3" has already been accounted for previously for "18".... but not the "5"...
So LCM = 2 x 3 x 3 x 5 = 18 x 5 = 90 minutes....
Starting time 12 noon....
After 90 minutes have elapsed, the time will be 1:30 p.m.
So at 1:30 p.m., both will be broadcast at the same time.
PROBLEM 2:
Now in order to find how many identical necklaces... find the factors of 90 and then 108
90 = 2 x 3 x 3 x 5
108 = 2 x 2 x 3 x 3 x 3
The way you get the most necklaces is to have the fewest beads on the necklace
What are the common factors between 90 and 108?
90 = 2 x 3 x 3 x 5
108 = 2 x 2 x 3 x 3 x 3
They both have a 2... then both have two 3's.... So there will be 2 x 3 x 3 = 18 necklaces. Now whatever factors are left over, say for 90, is the number of green beads on each necklaces... and whatever factors are left over for 108 is the number of blue beads on each necklace.
# of identical necklaces = 2 x 3 x 3 = 18 identical necklaces...
# of green beads on each necklace = 5
# of blue beads on each necklace = 6
.... for a total of 11 beads on each necklace... (5 green and 6 blue)
Basically what you did was find the GCF... greatest common factor of both 90 and 108....
The largest number (GCF) that goes into both numbers is 18... and that's the total number of necklaces...
Hope this helps! VERY GOOD questions that you asked. They really make the mind think! =)
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