Question

2021-08-04

Let x be the number of seats on the plane. The number of people in the plane is \(\displaystyle{\left(\frac{{2}}{{3}}\right)}{x}\) since it is two-thirds full.

boys+girls+women+men=(2/3)x \(\displaystyle{\left({0.2}\cdot{\left(\frac{{2}}{{3}}\right)}{x}\right)}+{\left(\frac{{1}}{{4}}\right)}{\left(\frac{{2}}{{3}}\right)}{x}+{\left(\frac{{1}}{{8}}\cdot\frac{{2}}{{3}}\right)}{x}+{68}={\left(\frac{{2}}{{3}}\right)}{x}\) \(\displaystyle{\left(\frac{{1}}{{5}}\right)}{\left(\frac{{2}}{{3}}\right)}{x}+{\left(\frac{{1}}{{4}}\right)}{\left(\frac{{2}}{{3}}\right)}{x}+{\left(\frac{{1}}{{8}}\right)}{\left(\frac{{2}}{{3}}\right)}{x}+{68}={\left(\frac{{2}}{{3}}\right)}{x}\) \(\displaystyle{\left(\frac{{2}}{{15}}\right)}{x}+{\left(\frac{{1}}{{6}}\right)}{x}+{\left(\frac{{1}}{{12}}\right)}{x}+{68}={\left(\frac{{2}}{{3}}\right)}{x}\)

Multiply both sides by the LCD which is 60:

\(\displaystyle{8}{x}+{10}{x}+{5}{x}+{4080}={40}{x}\)

\(\displaystyle{23}{x}+{4080}={40}{x}\)

\(\displaystyle{4080}={17}{x}\)

\(\displaystyle{x}=\frac{{4080}}{{17}}\)

x=240

So, there are 240 seats on the plane.

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