A theater purchases $500 worth of Sticky Bears and chocolate bombs. Each bag of Sticky Bears costs $1.50 and each bag of Chocolate Bombs costs $1.00. If a total of 400 bags of candy were purchased, how many bags of Chocolate Bombs did the theater buy?

Let

S=number of bags of sticky bears, then
400-S=number of bags of chocolate bombs.

From total cost = $500, we get
1.5S+1.0(400-S)=500
Solve for S
0.5S = 500-400
S=200

Quick way:
each bag of sticky bears costs 1.50
each bag of chocolate costs 1.00
Average cost = $500/400=1.25
which is smack in between 1.00 and 1.50.
So equal number of bags of each, namely 200.

Let's solve the problem step by step.

1. First, find the total cost of the Sticky Bears. Since each bag costs $1.50 and the theater purchased 400 bags in total, the total cost of the Sticky Bears is 1.50 * 400 = $<<1.50*400=600>>600.

2. Next, find the total cost of the Chocolate Bombs. Since the total cost of all the candy purchased is $500 and the total cost of the Sticky Bears is $600, the total cost of the Chocolate Bombs is 500 - 600 = $<<500-600=-100>>-100.

3. Since the total cost of the Chocolate Bombs is negative, it means there is no cost for the Chocolate Bombs, which implies that the theater did not buy any bags of Chocolate Bombs.

Therefore, the theater did not buy any bags of Chocolate Bombs.

To find the number of bags of Chocolate Bombs purchased, we need to set up an equation.

Let's assume the number of bags of Sticky Bears purchased is 'x'.
Since the total number of bags purchased is 400, we can set up the following equation:

x + y = 400

Here, 'y' represents the number of bags of Chocolate Bombs purchased.

Now, let's consider the cost of each type of candy. Each bag of Sticky Bears costs $1.50, and each bag of Chocolate Bombs costs $1.00.

The total cost of Sticky Bears can be calculated as 1.5x (since each bag costs $1.50).

The total cost of Chocolate Bombs can be calculated as 1y (since each bag costs $1.00).

According to the problem, the total cost of both types of candy is $500. Therefore, we can set up the equation:

1.5x + 1y = 500

Now we have a system of equations:

x + y = 400 (equation 1)
1.5x + 1y = 500 (equation 2)

To solve this system of equations, we can use any method like substitution or elimination. I will use the elimination method to find the value of 'y'.

Multiplying equation 1 by -1.5, we get:
-1.5x - 1.5y = -600 (equation 3)

Now, let's add equation 2 and equation 3:
(1.5x + 1y) + (-1.5x - 1.5y) = 500 + (-600)

Simplifying the equation, we get:
0x - 0.5y = -100

This can be further simplified as:
-0.5y = -100

To find the value of 'y', we divide both sides of the equation by -0.5:
y = (-100) / (-0.5)

This gives us:
y = 200

Therefore, the theater purchased 200 bags of Chocolate Bombs.