A digital camera is 1/4 full. It is 2/3 full after taking 374 additional photos. How many photos can the camera hold? How many photos were on the camera when it was 1/4 full?

Call X the full capacity of the camera in number of photos. So, when it is 1/4 full it has (1/4)X photos. Lets say that 1/4 full is a number A of photos, so:

(1/4)X = A

Then, you took 374 additional photos and it got 2/3 full. It is, you got, in total, (2/3)X photos, that we will call B photos.

(2/3)X = B

But, we also know that this (2/3)X photos is the sum of the previous (1/4)X photos (or A) plus some other 374 photos. So:

(2/3)X = (1/4)X + 374

As we have one term with X in each side, we woul like to pass all the X's to one only side. For this, sum -(1/4)X in both sides:

(2/3)X - (1/4)X = (1/4)X + 374 - (1/4)X

Operating with fractions:

(8/12)X - (3/12) X = 374

(5/12) X = 374

Multiplying both sides by (12/5) [or dividing by 5/12] to eliminate the (5/12):

X = 374 (12/5)

X = 897.6

The full capacity is 897.6 photos and when the camera was 1/4 full it had 224.4 photos.

You can verify by doing 224.2 + 374 = 598.4 and (2/3)*897.6=598.4