Passes for a music festival cost $95 for a family or $42 for individuals. There were 188 passes sold in total. How many of each type of pass was sold if the festival brought in $12,507

Let's solve this step by step.

We have two types of passes:
- Family passes cost $95 each.
- Individual passes cost $42 each.

We know:
- A total of 188 passes were sold.
- The total revenue was $12,507.

Let:
- $ x $ be the number of family passes sold.
- $ y $ be the number of individual passes sold.

We now have the following system of equations:

1. $ x + y = 188 $  (the total number of passes sold)
2. $ 95x + 42y = 12,507 $ (the total revenue equation)

### Step 1: Solve one equation for one variable
From equation (1), solve for $ y $:

\[
y = 188 - x
\]

### Step 2: Substitute this into the second equation
Substitute $ y = 188 - x $ into the second equation:

\[
95x + 42(188 - x) = 12,507
\]

### Step 3: Simplify and solve for $ x $
First, distribute the 42:

\[
95x + 42(188) - 42x = 12,507
\]

\[
95x + 7,896 - 42x = 12,507
\]

Now combine like terms:

\[
(95x - 42x) + 7,896 = 12,507
\]

\[
53x + 7,896 = 12,507
\]

Subtract 7,896 from both sides:

\[
53x = 12,507 - 7,896
\]

\[
53x = 4,611
\]

Now solve for $ x $:

\[
x = \frac{4,611}{53}
\]

\[
x = 87
\]

### Step 4: Solve for $ y $
Substitute $ x = 87 $ back into the first equation:

\[
87 + y = 188
\]

\[
y = 188 - 87
\]

\[
y = 101
\]

### Final Answer:
- 87 family passes were sold.
- 101 individual passes were sold.

### Check:
- Revenue from family passes: $ 87 \times 95 = 8,265 $
- Revenue from individual passes: $ 101 \times 42 = 4,242 $
- Total revenue: $ 8,265 + 4,242 = 12,507 $, which matches the given total.

Would you like more details on this solution? 

Here are 5 related questions:
1. How would the solution change if the individual passes cost $50 instead?
2. What if the total number of passes sold was 200 instead of 188?
3. How would the system of equations change if there was a third type of pass introduced?
4. Can you set up a similar system of equations for a different type of event, like a sporting event?
5. What happens to the solution if the revenue was overestimated by $1,000?

**Tip:** Always check your solution by substituting the values back into the original equations.

Passes for a music festival cost $95 for a family or $42 for individuals. There were 188 passes sold in total. How many of each type of pass was sold if the festival brought in $12,507?

Learn how to solve a system of equations to determine the number of family and individual passes sold for a music festival. This algebra problem involves solving two linear equations based on ticket prices and total sales, suitable for students in Grades 9-12.

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