Question 1105576
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  {{{4b/5+t/4+b/20}}} and Tom has {{{t+b/5-t/4-b/20}}}.  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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{{{4b/5+t/4+b/20=t+b/5-t/4-b/20}}}
LCD 20 so multiply both members by 20.


{{{16b+5t+b=20t+4b-5t-b}}}
{{{14b=10t}}}
{{{7b=5t}}}
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Use {{{b+t=144}}} and substitute for t.
{{{7b=5(144-b)}}}
{{{7b=5*144-5b}}}
{{{12b=5*144}}}
{{{b=5*12}}}
{{{highlight(b=60)}}}--------------original amount Ben had.


{{{t=144-60}}}
{{{highlight(t=84)}}}------------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
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{{{b-b/5}}} and {{{t+b/5}}}, Ben and Tom

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{{{b-b/5+(t+b/5)/4}}} and {{{t+b/5-(t+b/5)/4}}}, Ben and Tom


Now these last two numbers are given as equal.
{{{b-b/5+(t+b/5)/4=t+b/5-(t+b/5)/4}}}


{{{b-b/5+t/4+b/20=t+b/5-t/4-b/20}}}


LCD is 20, so multiply both sides by 20.


{{{20b-4b+5t+b=20t+4b-5t-b}}}


{{{17b+5t=23b-5t}}}


{{{10t=6b}}}


{{{5t=3b}}}


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Make substitution from {{{b+t=144}}}
{{{b=144-t}}}
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{{{5t=3(144-t)}}}
{{{5t=-3t+432}}}
{{{8t=432}}}
{{{cross(t=54)}}}-------------Tom had originally.


{{{cross(b=90)}}}------------Ben had originally.