On a certain transatlantic crossing, 20 percent of a ship's passengers held round-trip tickets...

Question

On a certain transatlantic crossing, 20 percent of a ship's passengers held round-trip tickets and also took their cars aboard the ship. If 60 percent of the passengers with round-trip tickets did not take their cars aboard the ship, what percent of the ship's passengers held round-trip tickets?

GMAT Panda · Accepted Answer

50% We first create an unknown for the percentage of passengers who held round-trip tickets. R=percent of passengers with round-trip tickets We translate "60 percent of the passengers with round-trip tickets did not take their cars aboard the ship", which means that the remaining percent of those passengers did take their cars. R-60/100R=40/100R We translate "20 percent of the ship's passengers held round-trip tickets and also took their cars aboard the ship" as the fraction of all passengers who both held round-trip tickets and took their cars. 40/100R=20/100 We solve the linear equation for the unknown by isolating it. 40/100R=20/100 R=20/10040/100 =20/40 =1/2=50%

Explanation	Calculations	Help
$We first create an unknown for the percentage of passengers who held round-trip tickets.$	$R = percent of passengers with round-trip tickets$
$We translate "60 percent of the passengers with round-trip tickets did not take their cars aboard the ship", which means that the remaining percent of those passengers did take their cars.$	$R - \frac{60}{100} R = \frac{40}{100} R$
$We translate "20 percent of the ship's passengers held round-trip tickets and also took their cars aboard the ship" as the fraction of all passengers who both held round-trip tickets and took their cars.$	$\frac{40}{100} R = \frac{20}{100}$
$We solve the linear equation for the unknown by isolating it.$	$\frac{40}{100} R = \frac{20}{100} R = \frac{\frac{20}{100}}{\frac{40}{100}} = \frac{20}{40} = \frac{1}{2} = 50%$

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