Zeke has swim club every 2 days and robotics club every 8 days. This month, he has swim club on the 2nd day of the month and robotics club on the 8th day of the month.
Zeke says that the first time he will have both clubs on the same day is the 16th day of the month because the LCM of 2 and 8 is 16.

Does Zeke’s reasoning make sense? Use the drop-down menus to explain.

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Zeke found the LCM to be the product of
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,

but because 8 is a
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of 2, the LCM is
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.

So the first day he will have both clubs is the
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day of the month.

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.

step-by-step explanation:

1. perpendicular

2. parallel

3. perpendicular