Question

1. emily predicted her car payment to be $250 each month. her actual car payment is $275 each month. enrique predicted his car payment to be $200 each month. his actual car payment is $225 each month.

a. by what percent was emily’s prediction off?
b. by what percent was enrique’s prediction off?

Explanation:

Step1: Calculate the absolute error for Emily

The formula for absolute error is \(| \text{Predicted} - \text{Actual} |\). For Emily, \(\text{Predicted}=250\), \(\text{Actual}=275\). So, \(|250 - 275|=25\)

Step2: Calculate the percent error for Emily

The formula for percent error is \(\frac{\text{Absolute Error}}{\text{Actual}}\times100\%\). Substitute the values: \(\frac{25}{275}\times 100\%=\frac{2500}{275}\%=\frac{100}{11}\%\approx9.09\%\)

Step3: Calculate the absolute error for Enrique

For Enrique, \(\text{Predicted}=200\), \(\text{Actual}=225\). So, \(|200 - 225| = 25\)

Step4: Calculate the percent error for Enrique

Using the percent - error formula \(\frac{\text{Absolute Error}}{\text{Actual}}\times100\%\). Substitute the values: \(\frac{25}{225}\times100\%=\frac{2500}{225}\%=\frac{100}{9}\%\approx11.11\%\)

Answer:

a. Emily's prediction was off by approximately \(9.09\%\)
b. Enrique's prediction was off by approximately \(11.11\%\)