Sue had half as many as Fred, Pat had a third as many as Sue. Altogether they had 216. How many did each have?

Question

Apples or Oranges or whatever. I wonder what they'll probably do with 216 apples hehe :)

Jokes apart, I really need to know how we can probably solve this question.

I did try to do it. I assumed sue had x apples. So, Fred has 2x apples (as sue has half as many as fred)
Also, pat had a third as many as sue.
So, pat probably has x/3.
Altogether, they had 216 apples.
i.e. x+2x+(x/3)=216.
I calculated the whole stuff and the value of x turned out to be 64.8 (wtf?)
Now, that's weird. I just need to know whether my method id right or not. Even if it is, then where did I goof up?
Thanks a ton :) :)

Answer 1

Why not look at it from the other direction, e.g. -



Pat has 1 share

Sue has 3 shares = 3 times as many as Pat

Fred has 6 shares = two times as many as Sue

Total 10 shares therefore 1 share is worth 21.6 so



Pat has 21.6

Sue has 64.8 i.e 3 x Pat's

Fred has 129.6 i.e 2 x Sue's



21.6 + 64.8 + 129.6 = 216 according to me, (but then I'm only 80 and can't use a calculator) - so your 64.8 was correct for Sue.

Answer 2

You are correct. Fred had 129.6. Sue had 64.8 (1/2 what Fred had). Pat had 21.6 (1/3 what Sue had).



129.6

64.8

21.6

Total 216

Answer 3

Pat had 36, Sue has 72, and Fred had 108.



Total is 216.



half of 216 is 108. that 108 for fred and 108-(Pat's) is what Sue has.



A third of 108 is 36. So Pat has 36.



108-36 is 72. So Sue has 72.