Apitcher of water is three-fourths full. five cups of water are served from the pitcher. then the pitcher is two-thirds full. how many cups of water can the pitcher hold?

Total quantity of water in the pitcher = 3/4
Number of cups served from the pitcher = 5
Quatity of water in the pitcher after serving 5 cups = 2/3
Then
The amount of water that is served by 5 cups = (3/4) - (2/3)
                                                                         = (9 - 8)/12
                                                                         = 1/12
So
The amount of water that is served by each cup = (1/12)/5
                                                                             = 1/60
Then
The number of cups serving 1/60 quantity of water = 1
The number of cups served by 3/4 quantity of water = [1/(1/60)] * (3/4)
                                                                                    = 60 * (3/4)
                                                                                     = 15 * 3
                                                                                    = 45 cups
So the total number cups of water that the pitcher can hold is 45.  hope the process of doing this problem is clear to you.