Question 1209504
**1. Set up the equations:**

* Let 'x' be the cost of one diary.
* Then, the cost of one book is 'x + $3.30'.

* Jamie spent 3/4 of her money on 3 books. 
    * Cost of 3 books: 3 * (x + $3.30) 
    * Fraction of money spent by Jamie: 3/4

* Grace spent 5/9 of her money on 2 diaries.
    * Cost of 2 diaries: 2 * x
    * Fraction of money spent by Grace: 5/9

* Since they had the same amount of money left, the fractions of money they spent must be equal:
    * (Cost of 3 books) / (Fraction spent by Jamie) = (Cost of 2 diaries) / (Fraction spent by Grace)
    * [3 * (x + $3.30)] / (3/4) = (2 * x) / (5/9)

**2. Solve the equation:**

* Simplify the equation:
    * 4 * (3x + $9.90) = (18/5) * 2x
    * 12x + $39.60 = (36/5) * x

* Isolate 'x':
    * 12x - (36/5) * x = -$39.60
    * (60x - 36x) / 5 = -$39.60
    * 24x = -$39.60 * 5
    * 24x = -$198
    * x = -$198 / 24
    * x = -$8.25 

* **Cost of one diary: -$8.25** 
* **Cost of one book:** -$8.25 + $3.30 = -$4.95

**3. Calculate the total money they had:**

* Since the cost of a diary is negative, there seems to be an error in the problem statement. 
* Assuming the problem is solvable, you would use the cost of a diary (x) and the fraction of money spent by either Jamie or Grace to calculate their initial amount of money. 
* Then, you would add the amounts of money Jamie and Grace initially had to find the total.

**Therefore, based on the given information, there appears to be an error in the problem, as the calculated cost of a diary is negative.**