Problem solving help...

[ramonsa]

Hello,

If 6 gallons of gasoline are added to a tank that is already filled to 3/4 of its capacity, the tank is then filled to 9/10 of its capacity. How many gallons does the tank hold?
(A) 20
(B) 24
(C) 36
(D) 40
(E) 60
Thanks

[ssmiles08]

Let x be the total capacity:

(3/4)*x + 6 = (9/10)*x

(3/20)*x = 6

x = 40

(D)

[VP_Jim]

Like the other question you just posted, this is another great candidate for backsolving. In my opinion, good backsolving questions are short word problems with numbers in the answer choices.

Let's try 40 gallons. A 40 gallon tank 3/4 full is 30 gallons. Add 6 to that and we're up to 36, which is 9/10 of 40. So, that's the right answer.

A trick: I assumed that the answer must "work nicely" with both the 3/4 fraction and the 9/10 fraction. Therefore, the answer must be divisible by both 4 and 10. Only A, D, and E fit the bill, so I would go under the assumption that one of those is the answer.

And, a note: there's absolutely nothing wrong with using equations on such problems. I just like to give alternate perspectives.