Ms. Banacka purchased a total of 25 items and spent $95.
Since each package of water balloons costs $3.25 and each water gun cost $4.50, we can calculate the total cost of the water balloons and water guns together.
Total cost of water balloons = 3.25 x number of packages of water balloons purchased
Total cost of water guns = 4.50 x number of water guns purchased
Total cost of all items = number of packages of water balloons x 3.25 + number of water guns x 4.50
Since the total cost of all items is $95 and the total cost of the water balloons is 3.25 x number of packages of water balloons purchased, we can set up the following equation:
3.25 x number of packages of water balloons purchased + number of water guns x 4.50 = 95
To solve this equation, we can first calculate the total cost of the water guns by subtracting the total cost of all items ($95) from the total cost of the water balloons (3.25 x number of packages of water balloons purchased):
number of water guns x 4.50 = 95 - 3.25 x number of packages of water balloons purchased
Now we can solve for number of water guns:
number of water guns = (95 - 3.25 x number of packages of water balloons purchased) / 4.50
We know that the total number of items purchased is 25, so the number of water guns must be equal to 25 minus the number of packages of water balloons purchased:
number of water guns = 25 - number of packages of water balloons purchased
Substituting this expression for number of water guns in our original equation gives us
3.25 x number of packages of water balloons purchased + (25 - number of packages of water balloons purchased) x 4.50 = 95
Now we can solve for number of packages of water balloons purchased:
number of packages of water balloons purchased = (95 - 25 x 4.50) / (3.25 - 4.50)
Simplifying, we get
number of packages of water balloons purchased = 16
Therefore, Ms. Banacka purchased 16 packages of water balloons.