Question

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.

Answer 1

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.