A total of 612 tickets were sold for the school play. They were either adult tickets or student tickets. There were 62 more student tickets sold than adult tickets. How many adult tickets were sold?


We can solve this problem using a system of equations.

Let:
- $ x $ be the number of adult tickets sold.
- $ y $ be the number of student tickets sold.

From the problem, we know two things:
1. The total number of tickets sold is 612:
   \[
   x + y = 612
   \]
2. There were 62 more student tickets sold than adult tickets:
   \[
   y = x + 62
   \]

### Step 1: Substitution
Substitute the second equation $ y = x + 62 $ into the first equation $ x + y = 612 $:
\[
x + (x + 62) = 612
\]

### Step 2: Simplify and solve for $ x $
\[
2x + 62 = 612
\]
Subtract 62 from both sides:
\[
2x = 550
\]
Now, divide by 2:
\[
x = 275
\]

### Step 3: Solve for $ y $
Substitute $ x = 275 $ into the equation $ y = x + 62 $:
\[
y = 275 + 62 = 337
\]

Thus, the number of adult tickets sold is $ \boxed{275} $, and the number of student tickets sold is $ 337 $.

Would you like more details or have any questions?

Here are 5 related questions:
1. If 100 fewer tickets were sold, how many adult tickets would be sold?
2. What percentage of the tickets were adult tickets?
3. If the total revenue from adult tickets was $825, how much was each adult ticket?
4. How many tickets would need to be sold to have an equal number of adult and student tickets?
5. If an additional 50 student tickets were sold, how many tickets in total would be sold?

**Tip**: When working with systems of equations, substitution can often simplify the problem if one variable is already isolated.

A total of 612 tickets were sold for the school play. They were either adult tickets or student tickets. There were 62 more student tickets sold than adult tickets. How many adult tickets were sold?

Learn how to solve a system of equations problem involving ticket sales. A total of 612 tickets were sold, with 62 more student tickets than adult tickets. This step-by-step solution uses substitution to find the number of adult and student tickets sold. Suitable for Grades 6-8.

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