Admission to a baseball game is $3.50 for general admission and $6.50
 for reserved seats.  The receipts were $5848.00
 for 1358 paid admissions.  How many of each ticket were sold?  (Round to nearest integer if necessary.)

Let:
- $ x $ be the number of general admission tickets sold.
- $ y $ be the number of reserved seat tickets sold.

We are given the following information:
1. The total number of tickets sold was 1358, so:
   \[
   x + y = 1358
   \]
2. The total receipts from ticket sales was $5848. Since general admission tickets are $3.50 and reserved seat tickets are $6.50, the total receipts can be written as:
   \[
   3.50x + 6.50y = 5848
   \]

### Step 1: Solve the system of equations
The system of equations is:
1. $ x + y = 1358 $
2. $ 3.50x + 6.50y = 5848 $

#### Solve equation (1) for $ y $:
\[
y = 1358 - x
\]

#### Substitute this into equation (2):
\[
3.50x + 6.50(1358 - x) = 5848
\]
Simplify:
\[
3.50x + 6.50 \times 1358 - 6.50x = 5848
\]
\[
3.50x + 8827 - 6.50x = 5848
\]
\[
-3x + 8827 = 5848
\]
\[
-3x = 5848 - 8827
\]
\[
-3x = -2979
\]
\[
x = \frac{-2979}{-3} = 993
\]

### Step 2: Find $ y $:
\[
y = 1358 - 993 = 365
\]

### Final Answer:
- The number of general admission tickets sold is 993.
- The number of reserved seat tickets sold is 365.

Would you like more details on this process?

Here are 5 related questions for further practice:
1. How would the problem change if general admission tickets cost $4.00 instead?
2. What if the total number of tickets sold was 1500, with the same pricing?
3. How do you check if the solutions satisfy both original equations?
4. Can you graph the system of equations to visualize the solution?
5. How would the solution change if both ticket types cost the same?

**Tip**: When solving word problems with systems of equations, always define your variables clearly to avoid confusion later in the problem.

Admission to a baseball game is $3.50 for general admission and $6.50 for reserved seats. The receipts were $5848.00 for 1358 paid admissions. How many of each ticket were sold? (Round to nearest integer if necessary.)

Learn how to solve a system of linear equations to find the number of general admission and reserved seat tickets sold for a baseball game, with given ticket prices of $3.50 and $6.50. The problem includes solving for 1358 tickets and $5848 in receipts. Suitable for Grades 8-10.

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