Julia spends 5/9 of her summer vacation at summer camp. she spends 3/4 of the remaining time at her grandparents home. the remaining 7 days she spends at the seashore with her family. how many days of summer vacation does she get each summer.

Let us assume the the number of days Julia gets as summer vacation each year = x
The number of days Julia spends in the summer camps = 5x/9
The number of days remaining after spending days
in summer camp = [x - (5x/9)]
                             = (9x - 5x)/9
                             = 4x/9
Then
Number of days Julia spends with her grandparents = [(3/4) * (4x/9)]
                                                                                    = x/3
The number of days Julia spends at the seashore with her family = 7
Then the equation will stand as written below
(5x/9) + (x/3) + 7 = x
5x + 3x + 63 = 9x
8x + 63 = 9x
63 = 9x - 8x
63 = x
x = 63
Then the total number of days Julia gets as her summer vacation is 63 days.