SOLUTION: Hi ben and tom had a total of 144 sweets.ben gave tom 1/5 of what he had. Tom the gave ben 1/4 of what he had to ben. If both had an equal number of sweets in the end, how many di

Question 1105576: Hi
ben and tom had a total of 144 sweets.ben gave tom 1/5 of what he had. Tom the gave ben 1/4 of what he had to ben. If both had an equal number of sweets in the end, how many did each of them have at first.
Thanks
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
RETRY---------------------

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ben gave tom 1/5 of what he had. Tom the gave ben 1/4 of what he had to ben.
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After that process is done,
Ben has and Tom has . These values are given as equal and their equality can be simplified.

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If both had an equal number of sweets in the end, how many did each of them have at first.
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LCD 20 so multiply both members by 20.

-
Use and substitute for t.

--------------original amount Ben had.

------------original amount Tom had.

***********************(BELOW STILL CONTAINS UNFIXED MISTAKE)******************************

Follow the description step-wise literally.

b, Ben had originally
t, Tom had originally

b+t=144
-
and , Ben and Tom
-
and , Ben and Tom

Now these last two numbers are given as equal.

LCD is 20, so multiply both sides by 20.

-
Make substitution from

-

-------------Tom had originally.

------------Ben had originally.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

There was an error in the algebra in the solution provided by the other tutor; the given answer does not satisfy the conditions in the problem.

Let b and t represent the numbers Ben and Tom start out with, respectively:
Start:
Ben = b;
Tom = t.

Ben gives 1/5 of the number he has to Tom; after that:
Ben = (4/5)b;
Tom = t+(1/5)b.

Tom now gives 1/4 of what he has -- which is (1/4)t+(1/20)b -- to Ben; after that:
Ben = (4/5)b+(1/4)t+(1/20)b = (17/20)b+(1/4)t;
Tom = (3/4)t+(3/20)b.

At this point the two of them have the same number of sweets, 72.

Ben:
(1)
Tom:
(2)

Solve (1) and (2) by elimination:

Ben started with 60 sweets; Tom with 84.

Check:
Start: Ben 60, Tom 84
After Ben gives 1/5 of his to Tom: Ben 60-12 = 48; Tom 84+12 = 96
After Tom gives 1/4 of his to Ben: Ben 48+24 = 72; Tom 96-24 = 72

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