SOLUTION: Hi A box of sweets is shared between A B C in the ratio of 3:4:5 B receives 48 sweets. C shares some of his sweets with his brothers. After sharing the ratio A B C is 12;16;

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Question 1152863: Hi
A box of sweets is shared between A B C in the ratio of 3:4:5 B receives 48 sweets.
C shares some of his sweets with his brothers. After sharing the ratio A B C is
12;16;15.
Find the number of sweets C shared with his brothers.
Thanks
Found 4 solutions by josgarithmetic, jim_thompson5910, ikleyn, greenestamps:
Answer by josgarithmetic(39616)   (Show Source): You can put this solution on YOUR website!
Just as a start the initial ratio is this:
A  :  B  :  C
 3 :  4  :  5
36 : 48  : 60

B having 48 initially, is 12 times as much as "4".
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!

A box of sweets is shared between A B C in the ratio of 3:4:5, so this means
A recieves 3/12 of the total
B recieves 4/12 of the total
C recieves 5/12 of the total
note that 3+4+5 = 12

Since B got 48 pieces, and B got 4/12 of the total, we know that,
x = total number of candies
B = amount B gets
B = (4/12)*x
48 = (4/12)*x
(4/12)*x = 48
(1/3)*x = 48
x = 3*48
x = 144
There are 144 candies total.

------------------------------------
Now turn to the information that the ratio of A:B:C updates to 12:16:15 after C shares his some of sweets.

This means,
A receives 12/43 of the total
B receives 16/43 of the total
C receives 15/43 of the total
we have 12+16+15 = 43

Assuming the total has not changed, then,
A = (12/43)*x
A = (12/43)*144
A = 40.186046511628
But this is not a whole number

So it is possible that your teacher made a typo when coming up with the ratios.

Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.

You are given that the original distribution of sweets was 3:4:5 between A, B and C.


It means, in translation to human language, that A, B and C possessed 3x, 4x and 5x sweets, respectively,

where x is the common measure of these quantities, now unknown.


But, in addition, you know from the condition  that 4x = 48  sweets that B had.

    Therefore, x = 48/4 = 12.

Hence, A, B and C had initially 3x = 3*12 = 36 sweets, 4x = 4*12 = 48 sweets and 5*x = 5*12 = 60 sweets, respectively.



    Half of the problem is just solved. Now we should analyse the second half.



After C shared his sweets with the brothers, the proportion became 12:16:15.


It means that now A, B and C possess 12y, 16y, and 15y of sweets, respectively.

Here y is the new common measure of their possessions, now unknown.


But we know that A still has 36 sweets, from the first half of the solution.

Hence, y = 36/12 = 3.  It implies that after sharing C possess 15*y = 15*3 = 45 sweets.


Hence,  60-45 = 15  is the number of sweets C passed to his brothers.   ANSWER

Solved.



Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!


The ratio initially is A:B:C = 3:4:5, with B having 48 sweets.

Any number of different calculations can be done to determine that A has 36 sweets and C has 60 sweets; and the total number of sweets is 144.

After C shares some of his sweets with A and B, the ratio is supposed to be A:B:C = 12:16:15.

But 144 sweets can't be divided in the ratio 12:16:15 -- so the problem is flawed.

If the ratio shown at the end of the problem is correct, then C didn't share any of his sweets with his brothers -- he simply ate some of his.



x has to be an integer for which 43x is less than 144; the maximum value is 3. That means the numbers of sweets are now 36, 48, and 45.

So A and B still have the numbers they started with; and C has 15 fewer.

And since I don't think he would have thrown them away, my guess is he ate them....
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