Word problem

184 is divided into two parts such that one-third of  one part may exceed 1/7th of  the  other part  is  8,then  what is  the greater  part ?
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1 Answer

Label one part A and the other part B so that A+B=184.

A/3-B/7=8,

A/3-(184-A)/7=8, multiply through by 21:

7A-3(184-A)=168,

7A-552+3A=168,

10A=168+552=720, A=72, B=184-72=112.

A third of A is 24 and a seventh of B is 16, so a third of A exceeds a seventh of B by 24-16=8.
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