Questions: According to the table above, in what month in 2021 is Jamie projected to reach 5,000 miles? According to the table above, if Pat had actually driven 16 percent more miles per month in 2021 than originally projected, as of the end of the day on June 30, 2021, how many more miles would he need to drive in order to be required to take a Defensive Driver Training class? a. 292 miles b. 535 miles c. 1,465 miles d. 1,816 miles

Solution Steps

Let \( J_i = 1146 \) be the miles traveled by Jamie since the last Defensive Driver Training class. The projected miles per month for Jamie is \( J_p = 512 \).

The target miles for Jamie to reach is \( T = 5000 \).

The number of months \( m \) needed for Jamie to reach the target can be calculated using the formula: \[ m = \frac{T - J_i}{J_p} = \frac{5000 - 1146}{512} \] Calculating this gives: \[ m \approx 7.4 \] Since months are counted in whole numbers, we round up to the next whole number, resulting in \( m = 8 \). Thus, Jamie is projected to reach 5000 miles in month 8.

Let \( P_i = 2941 \) be the miles traveled by Pat since the last Defensive Driver Training class. The projected miles per month for Pat is \( P_p = 254 \).

Pat's actual miles per month, considering a 16% increase, is given by: \[ P_a = P_p \times 1.16 = 254 \times 1.16 \]

The total miles driven by Pat over 6 months is: \[ P_d = P_i + (P_a \times 6) \]

The remaining miles \( R \) that Pat needs to drive to reach 5000 miles is calculated as: \[ R = T - P_d = 5000 - P_d \] After performing the calculations, it is determined that Pat needs to drive \( R \approx 291 \) more miles to be required to take a Defensive Driver Training class.

Final Answer