A total of 5 liters of gasoline is to be poured into two empty containers with capacities of 2...

Question

A total of 5 liters of gasoline is to be poured into two empty containers with capacities of 2 liters and 6 liters, respectively, such that both containers will be filled to the same percent of their respective capacities. What amount of gasoline, in liters, must be poured into the 6 -liter container?

GMAT Panda · Accepted Answer

33/4 We create a variable for the amount in the 6-liter container and express the amount in the 2-liter container in terms of that variable. x = amount poured into the 6-liter container 5 - x = amount poured into the 2-liter container We translate "filled to the same percent of their respective capacities" into the equality of their fill ratios. x/6 = 5 - x/2 We solve the linear equation by cross-multiplying and isolating x. 2x = 6(5 - x) 2x = 30 - 6x 8x = 30 x = 30/8 = 15/4 = 33/4 We conclude that the 6-liter container must receive this amount. x = 33/4

Explanation	Calculations	Help
$We create a variable for the amount in the 6-liter container and express the amount in the 2-liter container in terms of that variable.$	$x = amount poured into the 6-liter container 5 - x = amount poured into the 2-liter container$
$We translate "filled to the same percent of their respective capacities" into the equality of their fill ratios.$	$\frac{x}{6} = \frac{5 - x}{2}$
$We solve the linear equation by cross-multiplying and isolating x .$	$2 x = 6 (5 - x) 2 x = 30 - 6 x 8 x = 30 x = \frac{30}{8} = \frac{15}{4} = 3 \frac{3}{4}$
$We conclude that the 6-liter container must receive this amount.$	$x = 3 \frac{3}{4}$

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