Question

Divide 184 into two parts such that one -third of one part may exceed one -seventh of the other part by 8.

Answer 1

$let \: the \: parts \: be \: x \: and \: 184 - x \:. \:$
$thus \: \frac{1}{3} x = \frac{1}{7} x + 8 \\ \frac{1}{3} x - \frac{1}{7} x = 8 \\ 4x = 168 \\ x = 42 \\ thus \: parts \: are \: 42 \: and \: 142$