Question 1012530: There are two boxes p & q ,on a balance.both have unknown number of marbles.intially p is heavier than q. When 4 marbles are taken from box p & placed in box q, the balance tip over(means now q is heavier than p now). If we found the difference in the original number of marbles- that is, we subtracted the number of marbles in box q from the number in box p than what is the smallest and largest number we vould get would be...
Please help me i have no idea how to solve this type of question
Thanks
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! there are p marbles in the first box.
there are q marbles in the second box.
you are given that the first box is heavier than the second box.
since all the marbles weigh the same, this means the number of marbles in the first box is greater than the number of marbles in the second box.
that leads to:
p > q
you are also given that, if you remove 4 marbles from the first box and transfer them to the second box, that the number of marbles in the first box will now be heavier than the number of marbles in the second box.
that leads to:
p-4 < q+4
solve for p in this second equaation to get:
p < q + 8
this means that, whatever the value of q is, the value of p is less than 8 more than that.
so the most that p can be is 7 greater than q.
this comes from p < q + 8
the least that p can be is 1 greater than q.
this comes from p > q
i believe that answers the question.
here's a table that shows you all the calculations from p = q + 1 to p = q + 7
column 1 2 3 4 5 6
before................ after.......................
p q compare p q compare
q+0 q p = q q-4 q+4 p < q ***** note 1
q+1 q p > q q-3 q+4 p < q
q+2 q p > q q-2 q+4 p < q
q+3 q p > q q-1 q+4 p < q
q+4 q p > q q q+4 p < q
q+5 q p > q q+1 q+4 p < q
q+6 q p > q q+2 q+4 p < q
q+7 q p > q q+3 q+4 p < q
q+8 q p > q q+4 q+4 p = q ***** note 2
q+9 q p > q q+5 q+4 p < q ***** note 3
the conditions that have to be satisfied are:
p has to be greater than q before removing 4 from p and adding 4 to q.
see columns 1 to 3.
p has to be less than q after removing 4 from p and adding 4 to q.
see columns 4 to 6
if p-4 < q+4 is not satisfied, then p < q+8 is also not satisfied, because p < q+8 is derived from p-4 < q+4.
note 1:
p>q is not satisfied.
note 2:
p-4 > q+4 is not satisfied.
note 3:
p-4 > q+4 is not satisfied.
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