Let's call the total number of children in the class "x".
We know that x is between 20 and 30, so:
20 < x < 30
Next, we know that there are six times as many children between Anna and Zara going clockwise as there are going anti-clockwise.
Let's call the number of children going clockwise from Anna to Zara "y".
Then the number of children going anti-clockwise from Zara to Anna is y/6.
Now we can set up an equation:
y = 6(y/6)
This simplifies to y = y, which doesn't give us any new information.
However, we can use this equation to set up another equation involving the total number of children in the class:
y + y/6 + 2 = x
The "+2" at the end represents Anna and Zara themselves, who we've counted twice (once in the clockwise count and once in the anti-clockwise count).
Now we can solve for y:
y + y/6 + 2 = x
(7/6)y + 2 = x
y = (6/7)(x-2)
We know that y is a whole number, since it represents the number of children between Anna and Zara in one direction. Therefore, x-2 must be divisible by 7.
Let's try some values of x and see if they work:
If x = 21, then y = (6/7)(19) = 16.285, which isn't a whole number.
If x = 22, then y = (6/7)(20) = 17.143, which also isn't a whole number.
If x = 23, then y = (6/7)(21) = 18, which is a whole number.
Therefore, there are 18 children between Anna and Zara going clockwise, and 3 children going anti-clockwise.
We can check that this works with the other information we were given:
- There are 23 children total.
- 18 + 3 + 2 (Anna and Zara) = 23, so this checks out.
Therefore, the answer is that there are 23 children in Miss Tree's class.
There are more than 20 and fewer than 30 children in Miss Tree's class. They are all standing in a circle Anna notices that there are six times as many children between her and Zara going round the circle clockwise, as there are going round anti-clockwise. How many children are there in the class
5 answers
A------Z------------
....n..........6n
There are n+6n+2 = 7n+2 students
If n=3, 7n+2 = 23
No other value of n satisfies 20 < 7n+2 < 30
....n..........6n
There are n+6n+2 = 7n+2 students
If n=3, 7n+2 = 23
No other value of n satisfies 20 < 7n+2 < 30
That's correct! Thank you for providing a visual representation of the problem. It helps to see that there are "n" students between Anna and Zara going clockwise, and "6n" students going anti-clockwise. Using your diagram, we can see that there are 23 students in the class when "n" is 3. Well done!
Lol, I really don't think that oobleck needs any confirmation from you, dear bot, I think his reasoning powers would indeed far surpass that of the bot, judging from the absurd methods and solutions that the bot offers.
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5 answers