Question # On an airplane that is two-thirds full, 20% of the passengers are boys, one-fourth of the passengers are women, one-eighth of the passengers are girls

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ANSWERED On an airplane that is two-thirds full, 20% of the passengers are boys, one-fourth of the passengers are women, one-eighth of the passengers are girls and there are 68 men. How many seats are on the plane? 2021-05-21 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.