Jocelyn was given a box of assorted chocolates for her birthday. Each night, Jocelyn treats herself to some chocolates. The number of chocolates remaining in the box tt days after Jocelyn's birthday can be modeled by the equation C, equals, minus, 3, t, plus, 30, .C=−3t+30. What is the xx-intercept of the equation and what is its interpretation in the context of the problem?

The equation modeling the number of chocolates remaining after \( t \) days is:

\[
C = -3t + 30
\]

Where:
- \( C \) represents the number of chocolates left.
- \( t \) represents the number of days after Jocelyn's birthday.

### Finding the x-intercept:
The x-intercept is found by setting \( C = 0 \), because at the x-intercept, the number of chocolates left will be zero.

1. Set \( C = 0 \) in the equation:
   \[
   0 = -3t + 30
   \]

2. Solve for \( t \):
   \[
   3t = 30
   \]
   \[
   t = \frac{30}{3} = 10
   \]

### Interpretation:
The x-intercept occurs at \( t = 10 \), meaning that 10 days after Jocelyn's birthday, she will have no chocolates left. This implies that if she continues to eat chocolates at the same rate, the box will be empty after 10 days.

### Summary:
- The x-intercept is \( t = 10 \).
- Interpretation: Jocelyn will have no chocolates left after 10 days.

Do you want more details, or have any questions?

Here are 5 related questions for further exploration:
1. How many chocolates does Jocelyn eat each night?
2. How many chocolates were originally in the box?
3. What would happen if Jocelyn ate fewer chocolates each night?
4. How does the slope \( -3 \) affect the number of chocolates over time?
5. Can we model the same scenario if Jocelyn skips eating chocolates some days?

**Tip:** The x-intercept in any linear equation tells you when a quantity (here, chocolates) reaches zero!

Jocelyn was given a box of assorted chocolates for her birthday. Each night, Jocelyn treats herself to some chocolates. The number of chocolates remaining in the box tt days after Jocelyn's birthday can be modeled by the equation C = −3t + 30. What is the x-intercept of the equation and what is its interpretation in the context of the problem?

Learn how to find the x-intercept of the linear equation C = −3t + 30, representing the number of chocolates Jocelyn has left after t days. The solution walks through key concepts in linear equations and how the x-intercept indicates when she will run out of chocolates. Suitable for Grades 6-8.

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