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.

Question

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.

Answer 1

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.