Math Problem Statement

A movie house sells adult tickets and student tickets. On a recent night, there were 43 more adult tickets sold than student tickets, for a total of 209 tickets. How many student tickets were sold?

Solution

Let's define variables to solve this problem:

Let:

  • xx be the number of student tickets sold.
  • The number of adult tickets sold is x+43x + 43 since there are 43 more adult tickets than student tickets.

The total number of tickets sold is 209, so we can set up the equation:

x+(x+43)=209x + (x + 43) = 209

Simplifying the equation:

2x+43=2092x + 43 = 209

Now, subtract 43 from both sides:

2x=209432x = 209 - 43

2x=1662x = 166

Finally, divide by 2:

x=1662=83x = \frac{166}{2} = 83

Thus, 83 student tickets were sold.

Would you like a more detailed explanation, or do you have any further questions?

Here are 5 related questions for practice:

  1. If the total number of tickets was 250 instead of 209, how many student tickets would have been sold?
  2. What if there were 30 more adult tickets than student tickets with the same total of 209?
  3. How many adult tickets were sold on that night?
  4. What if the total number of tickets sold was 300, with 50 more adult tickets than student tickets?
  5. What percentage of the total tickets sold were student tickets?

Tip: When solving word problems, always define variables clearly and set up an equation based on the relationships described in the problem.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

x + (x + 43) = 209

Theorems

Basic properties of linear equations

Suitable Grade Level

Grades 6-8