Some Fruit Punch
There is a party tonight at the Puzzlaria Tavern and Ross asked me to get some orange juice and pineapple juice for the Fruit Punch he is preparing. Being already giddy with all the drinks I had had, I tried some mixing of my own. Grabbing the large orange juice jar (lets call it jar O), I added enough juice into the second jar containing pineapple juice (jar P) till its contents were doubled. Then, I poured some of the mixture back into jar O to double its contents.
Fairly sloshed now, I decide a good way to settle matters would be to again pour from Jar O into Jar P to double P’s contents and proceed to do so. At this point I realize there is an equal quantity of pineapple juice in each jar. If Jar P now has one more litre of orange juice than pineapple juice, can you tell this poor muddle-headed soul, how much more orange juice than pineapple juice there is in Jar O?
Help me! The party is in full swing and Ross is getting impatient !!
Labels: mathemagic, mathschallenge





16 Comments:
one litre
regards, Curtis
At start
jug O = 4L orange(o)
Jug P = 2L pineapple(p)
1st pour
jug O = 2o
jug P = 2p+2o
2nd pour
jug O = 2o+(1p+1o)= 3o+1p
jug P = 1p+1o
3rd pour
jug O = 1.5o+0.5p
jug P = 1p+1o+(1.5o+0.5p)=2.5o+1.5p
hence jug P contains one more litre of pineapple juice and one more litre of orange juice
regards, Curtis
But would be better with some vodka in it!!
Hi Curtis...that's not the right answer
half a litre
nope...
I too get 1 more litre of Orange juice than Pineapple juice in Jar O.
Start: Jar O = 4o, Jar P = 2p
Pour 1: Jar O = 2o, Jar P = 2p, 2o
Pour 2: Jar O = 3o 1p, Jar P = 1p, 1o
Pour 3: Jar O = 1.5o .5p, Jar P = 2.5o 1.5p
Jar P contains 1 more o than p, and answer, Jar O contains 1 more o than p.
OK Jin...i think i have it(or i'm way off)
Answer:there is 1.2 more liters of orange juice than pinapple juice in Jar O.
you started with 2,8L in Jar O and 1.2L in Jar P.
been at this ToM for longer than i'm willing to say
good one!
Still no winners....I think I know where Curtis and Ektahuna are making an error.
Will check out Knightmare's solution...
Knightmare...checked your solution out...it does not fulfill the problem condition that after 3 pourings, 'Jar P now has one more litre of orange juice than pineapple juice'.
Hi Jin,
Reading the question again, my answer doesn't hold true for there being equal quantities of pineapple juice at the end.....
.....back to the drawing board!
regards, Curtis
Got it!!
answer 3 litres
regards, Curtis
Start with 7 litre orange and 3 litre pineapple
this ratio 7:3 always gives equal pineapple juice at the end, so Knightmare had the right idea and I was able to steal that idea and see the ratio of orange to pineapple in jug P at the end was 5:3,
so for a difference of 1 litre, pineapple juice must = 1.5 litre, orange 2.5 litre, and worked back from there.
regards, Curtis
Yup Curtis, that is absolutely right...initially 7 litres orang juice and 3 litres pineapple juice.
After all the mixing, 3 more litres of orange than pineapple juice in Jar O.
oh,i see where i went wrong-answered for 1 litre of orange juice in Jar P-forgot the 1 litre "MORE" part
Ah yes, I missed the point that pineapple juice was equal too :(
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