see below for the question

Question

the gauge of an oil tank indicated that the tank was 1/7 full.  after 240 gallons of oil were added to the tank, the guage indicated that the tank was 4/7 full. how many gallons of oil does the tank hold assuming the gauge is acurate

Answer 1

If possible, assign a variable to the amount the problem asks you to find.  Here, let:

     x = gallons the tank holds

 

Translate:

  "tank ...1/7 full...after 240 gallons ... added to the tank, ...the tank was 4/7 full"   means

       (1/7)x                      + 240                                                            = (4/7)x

     240 = (3/7)x                [subtract (1/7)x from both sides]

     (7/3)240 = x            [multiply both sides by 7/3]

       560 gallons =  x

 

Checking (very important):

  Is  (1/7)560 + 240 = (4/7)560  ?

           80     +  240  =  320   ?

                 320   =   320    ? yes

Answer 2

Since the fraction went from 1/7 to 4/7, we can see that the 240 gallons takes up 3/7 of the tank. You can probably see that I got 3/7 by taking 4/7 - 1/7.

 

If x = the capacity of the tank, we know that 3/7 of the capacity is 240 gallons.

 

As an equation, this says that (3/7)x = 240. We need to solve for x.

 

The easiest way to un-do multiplication by a fraction is to multiply by its reciprocal. So we multiply both sides of the equation by  7/3.  I think you can take it from there.