
The Celebrity Theater  has 
1
,
260
1,260 large popcorn buckets left.   They sell an average of 
90
90 large popcorns a day.  Write a linear equation to represent the number of large popcorn buckets the Celebrity Theater has left after 
x
x days.



We are given the following information:

- The theater has 1,260 large popcorn buckets initially.
- They sell 90 large popcorn buckets per day on average.

Let \( x \) represent the number of days, and \( y \) represent the number of large popcorn buckets left after \( x \) days. The number of popcorn buckets will decrease by 90 each day, so the rate of change is -90.

We can write the linear equation in the slope-intercept form \( y = mx + b \), where:

- \( m \) is the rate of change (slope), which is -90,
- \( b \) is the initial amount of popcorn buckets, which is 1,260.

Thus, the linear equation is:

\[
y = -90x + 1260
\]

This equation represents the number of large popcorn buckets left after \( x \) days.

Would you like further explanation on how to apply this equation, or do you have other questions?

Here are five related questions:
1. How many large popcorn buckets will be left after 10 days?
2. After how many days will the Celebrity Theater run out of large popcorn buckets?
3. If the theater sold 100 popcorns a day instead, how would the equation change?
4. How does the slope of the equation affect the rate of selling popcorn buckets?
5. What would happen to the equation if more buckets were added to the stock?

**Tip:** In linear equations, the slope tells you how fast something changes over time (rate of change).

The Celebrity Theater has 1,260 large popcorn buckets left. They sell an average of 90 large popcorns a day. Write a linear equation to represent the number of large popcorn buckets the Celebrity Theater has left after x days.

Learn how to write a linear equation to represent the number of large popcorn buckets left after x days at Celebrity Theater. The theater starts with 1,260 buckets and sells 90 buckets per day. This problem introduces linear equations and key algebra concepts. Suitable for Grades 6-8.

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