Problem Solving

Hello, I'm having trouble with this question and appreciate explanations to solve.

Drum X is 1/2 full of oil and drum Y, which is twice the capacity of drum X, is 2/3 full of oil. If all the oil in drum X is poured into drum Y, then drum Y will be filled to what fraction of its capacity?

Answer is 11/12.

Thanks for your help.

Two ways to do this:

1) Assign quantities to the barrels and solve from there. Looking at the denominators, let the capacity of x = 6, so at half-full there are 3 units of oil in x. Y has twice the capacity of x, so y's capacity = 12, and 2/3 of 12 is 8, so there are 8 units of oil in y. 3 units in x + 8 units in y = 11 units in a 12 unit drum, so 11/12.

2) Algebraically: (Capacity of X * Level of X) + (Capacity of Y * Level of Y) = (1/2)(1/2) + (1)(2/3) = 1/4 + 2/3 = 11/12

Working through the second way, I think you fell into the trap of trying to set up your algebraical equation as (1/2) + (2)(2/3), right?

Take Drum X as 150 litres, Drum Y as 300 litres

Drum X has 75 litres (1/2 full), Drum Y has 200 litres (2/3 full)

Pour 75 litres into the 300 litre drum - you get 200+75 = 275 litres

275/300 -> Divide by 5

= 11/12

OMG! Duh! I can't believe I couldn't figure this out! Thank you!

Bhattu wrote:Take Drum X as 150 litres, Drum Y as 300 litres

Drum X has 75 litres (1/2 full), Drum Y has 200 litres (2/3 full)

Pour 75 litres into the 300 litre drum - you get 200+75 = 275 litres

275/300 -> Divide by 5

= 11/12

Ingenious!!!!!!!!!!!!!!!!!