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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.\newlineMr. Mitchell is contemplating which chauffeured car service to take to the airport. The first costs $29\$29 up front and $1\$1 per kilometer. The second costs $7\$7 plus $2\$2 per kilometer. For a certain driving distance, the two companies charge the same total fare. What is the distance? What is the total fare?\newlineFor a driving distance of km\text{km}, the total fare is $□\$\square.

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Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.\newlineMr. Mitchell is contemplating which chauffeured car service to take to the airport. The first costs $29\$29 up front and $1\$1 per kilometer. The second costs $7\$7 plus $2\$2 per kilometer. For a certain driving distance, the two companies charge the same total fare. What is the distance? What is the total fare?\newlineFor a driving distance of km\text{km}, the total fare is $□\$\square.
  1. Denote driving distance: Let's denote the driving distance in kilometers as d d . The total fare for the first service is 29+1d 29 + 1d , and for the second service, it is 7+2d 7 + 2d . We need to find the value of d d for which both services charge the same amount. So, we can set up the following system of equations:\newline11. 29+d=7+2d 29 + d = 7 + 2d - This equation represents the point at which both services cost the same.
  2. Set up system of equations: Now, we solve the equation for d d . We can subtract d d from both sides to get:\newline29=7+d 29 = 7 + d \newlineThen, we subtract 77 from both sides to isolate d d :\newline22=d 22 = d \newlineSo, the driving distance at which both services charge the same amount is 2222 kilometers.
  3. Solve for driving distance: To find the total fare, we can substitute d=22 d = 22 into either of the original equations. Let's use the first service's equation:\newlineTotal fare = 29+1×22 29 + 1 \times 22 \newlineTotal fare = 29+22 29 + 22 \newlineTotal fare = 51 51 \newlineSo, the total fare for both services at a driving distance of 2222 kilometers is $\(51\).

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