The equation y = 32.9x - 572.87 can be used to model the relationship between sales at a local ice cream shop. y, in dollars, and the outside temperature, x in degrees Fahrenheit (F). Complete the statements.

When the outside temperature is 30 degrees F, the sales are estimated to be___.
When the outside temperature is ___, the sales are estimated to be $1,993.33.

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 month ago

To complete the statements, we can substitute the given values into the equation \( y = 32.9x - 572.87 \).

1. **When the outside temperature is 30 degrees F:**
\[
y = 32.9(30) - 572.87
\]
\[
y = 987 - 572.87
\]
\[
y = 414.13
\]
So, when the outside temperature is 30 degrees F, the sales are estimated to be **$414.13**.

2. **When the sales are estimated to be $1,993.33:**
We need to solve for \( x \) when \( y = 1,993.33 \).
\[
1,993.33 = 32.9x - 572.87
\]
Add 572.87 to both sides:
\[
1,993.33 + 572.87 = 32.9x
\]
\[
2,566.20 = 32.9x
\]
Now, divide by 32.9:
\[
x = \frac{2,566.20}{32.9}
\]
\[
x \approx 77.94
\]
So, when the outside temperature is approximately **77.94 degrees F**, the sales are estimated to be $1,993.33.

### Summary of Answers
1. When the outside temperature is 30 degrees F, the sales are estimated to be **$414.13**.
2. When the outside temperature is approximately **77.94 degrees F**, the sales are estimated to be $1,993.33.