https://file.aiquickdraw.com/mathbot/file/1725634201432udzcfsid.jpg

The equation provided is:

\[
y = 32.9z - 572.87
\]

where:
- $ y $ represents sales (in dollars).
- $ z $ represents the outside temperature (in degrees Fahrenheit, °F).

We are tasked with completing the following statements:

1. When the outside temperature is 30°F, the sales are estimated to be $ y = $ ?
2. When the outside temperature is unknown, the sales are estimated to be $1,993.33, so find $ z $.

Let's solve these.

### 1. Sales at 30°F

Substitute $ z = 30 $ into the equation:

\[
y = 32.9(30) - 572.87
\]

Let me calculate this value.When the outside temperature is 30°F, the sales are estimated to be \$414.13.

### 2. Find the temperature when sales are \$1,993.33

We have the equation:

\[
y = 32.9z - 572.87
\]

Set $ y = 1,993.33 $ and solve for $ z $:

\[
1,993.33 = 32.9z - 572.87
\]

Let me calculate the value of $ z $.It seems like I can’t do more advanced data analysis right now. Please try again later. However, you can solve the equation by following these steps:

\[
1,993.33 = 32.9z - 572.87
\]

1. Add 572.87 to both sides:

\[
1,993.33 + 572.87 = 32.9z
\]

2. Divide by 32.9:

\[
z = \frac{1,993.33 + 572.87}{32.9}
\]

If you'd like, I can guide you through these calculations manually!

Would you like any more details? Here are some questions to explore further:

1. What happens to sales as the temperature increases beyond 100°F?
2. How would the equation change if the sales increase rate per degree was 35 instead of 32.9?
3. What temperature results in no sales according to this equation?
4. What are the implications of negative sales estimates for very low temperatures?
5. Can this model be adjusted for different types of shops, like coffee shops in winter?

**Tip:** For linear models, always check if the trend remains reasonable at extreme values (high or low).

The equation y = 32.9z - 572.87 can be used to model the relationship between sales at a local ice cream shop, y, in dollars, and the outside temperature, z, in degrees Fahrenheit (F). Complete the statements: When the outside temperature is 30°F, the sales are estimated to be ____. When the outside temperature is ____, the sales are estimated to be $1,993.33.

Learn how to use the linear equation y = 32.9z - 572.87 to estimate sales based on temperature. This problem involves key algebraic concepts and linear functions, making it suitable for students in Grades 8-10.

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