Word Problem

[AWow1980]

I can't seem to figure out how to set this problem up correctly. Can someone please help me?

1. Jake and Snake have a 360 day membership to a badminton club. Jake will use it every other day. Snake will use it every third day. They both use the club on day one. How many days total out of 360 will at least one of them use the club?

 

[wjm11]

I can't seem to figure out how to set this problem up correctly. Can someone please help me?

1. Jake and Snake have a 360 day membership to a badminton club. Jake will use it every other day. Snake will use it every third day. They both use the club on day one. How many days total out of 360 will at least one of them use the club?

For simplicity, let's assume they don't both start on day 1, but rather:

Jake: day 2, 4, 6, 8, 10, 12,...

Snake: day 3, 6, 9, 12,...

Notice which days they both go to the club? That happens on multiples of 6.

If the question only asked how many times Jake goes to the club, we would simple divide 360 by 2. Likewise, for Snake, we'd divide 360 by 3. Can you proceed from here?

 

[HallsofIvy]

Looks straight forward. Jake went to the gym on days 1, 3, 5, 7, 9, etc.- every odd numbered day. Snake went to the gym on days number 1, 4, 7, 10, 13, ... days of the form 3n+ 1, every other one of which is odd. How any days of the form 3n+1 are there in 365 days? How many of those are odd?

 

[lookagain]

... in 365 days?

The OP's question has it at 360 days.

 

[HallsofIvy]

The OP's question has it at 360 days.

Right, thanks. Actually I first wrote "360" then thought, "no, that's not right- there are 365 days in a year"!

So Snake goes to the gym on days 3n+1. How many such days are there in 360 days, and how many of those are odd?

 

[Deleted member 4993]

I can't seem to figure out how to set this problem up correctly. Can someone please help me?

1. Jake and Snake have a 360 day membership to a badminton club. Jake will use it every other day. Snake will use it every third day. They both use the club on day one. How many days total out of 360 will at least one of them use the club?

1.....3.....5.....7.....9....11....13....15....17....19....21....23....25......

1.....4.....7....10....13....16....19....22....25

so they are playing together on 1,7,13,19,25..... do you see a pattern (arithmatic series)

 

[lookagain]

1.....3.....5.....7.....9....11....13....15....17....19....21....23....25......

1.....4.....7....10....13....16....19....22....25

so they are playing together on 1,7,13,19,25..... do you see a pattern (arithmatic series)

AWow1980,

would you know how to use the total number of days they are playing together to answer your
question of how many days that at least one of them was using the club?

 

[Deleted member 4993]

I can't seem to figure out how to set this problem up correctly. Can someone please help me?

1. Jake and Snake have a 360 day membership to a badminton club. Jake will use it every other day. Snake will use it every third day. They both use the club on day one. How many days total out of 360 will at least one of them use the club?

Further hints:

# of days Jake went to club = 360/2 = 180

# of days Snake went to club = 360/3 = 120

# of days (Jake+Snake) went to club together = 360/(2*3) = 60

Now continue.......