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A highway has an optional toll lane that drivers may take to reduce the time they spend driving. Drivers pay a small fee to enter the toll lane ($0.25) . Then, once they leave the toll lane, they pay a fee based on the number of miles they have traveled on the toll lane. Assume that the driver may leave the lane after any whole number of miles and pays for exactly that number, without rounding up. Note that there is a linear relationship between the number of miles a vehicle has traveled and the price of the toll. A. If Frank is on the toll road for 7.00 miles and then leaves the lane, how much will he have to pay total for the trip? $ B. Each day, Susan has to pay a toll of $8.50 when she uses the toll lane to get to school. How many miles does Susan travel on the toll lane to get to school? mi C. John started a carpool with his coworkers to save money. He and his three passengers split the cost of the toll. If each person pays about $1.38 , which includes their contribution to the toll lane entry fee, how many miles do they travel on the toll lane? mi

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Answer:

A.$ 0.25 +7x

B. 8.25/x miles

C. 5.27/x  miles

Note : $x is the cost of using the toll lane per mile

Step-by-step explanation:

In this case, you are given;

Small fee to enter the toll lane= ($0.25)

Fee to leave the lane= miles covered × cost to travel the line per mile

Lets cost of using the lane per mile= $ x

A.

If Frank covers 7 miles on the lane, the cost will be;

=(Fee to enter lane) + (cost to use the lane per mile ×7)

=$0.25 + (x ×7)

= $ 0.25 +7x

B.

Payments made by Susan each day for using lane = $8.50

Fee of using lane =$0.25

Amount spent for using the lane= $8.50-$0.25 =$ 8.25

Cost of using the lane per mile= $x

Amount spent for using the lane =$8.25

Number of miles covered in the toll lane will be;

($8.25)÷ ($x)

= 8.25/x miles

C.

Number of passengers that used the car= 4 (John + 3 passengers)

Amount each contributed = $1.38

Total amount contributed by all passengers for using the toll lane= $1.38×4=$5.52

Subtract the fee for using the lane = $5.52-$0.25 =$5.27

Cost per mile for using the lane = $ x

Number of miles covered will be ;

$5.27/$x = 5.27/x  miles

If you know the value of x which is the cost of using the toll lane per mile, then you can substitute this value in the expressions to get exact figures.

The total amount Frank needs to pay is (0.25 + 7a), the number of miles covered by Susan in toll lane is ([tex]8.25\div a[/tex]) miles, and the number of miles covered by john and his coworkers is ([tex]5.27\div a[/tex]) miles and this can be determined by forming the linear equation with the help of the given data.

Given :

  • Drivers pay a small fee to enter the toll lane ($0.25).
  • Once they leave the toll lane, they pay a fee based on the number of miles they have traveled on the toll lane.
  • Assume that the driver may leave the lane after any whole number of miles and pay for exactly that number, without rounding up.

Let the cost of lane per mile be 'a'.

A) Given - Frank is on the toll road for 7.00 miles and then leaves the lane.

Total amount he needs to pay = 0.25 + 7a

B). Given - Susan has to pay a toll of $8.50 when she uses the toll lane to get to school.

Amount spend in lane = 8.50 - 0.25

                                     = $8.25

Number of miles covered in toll lane = ([tex]8.25\div a[/tex]) miles

C) Given - Each person pays about $1.38 , which includes their contribution to the toll lane entry fee.

Total number of the person in the car = 4

Total amount contributed = [tex]1.38 \times 4[/tex] = $5.52

Amount remain after subtracting the amount of using the lane = 5.52 - 0.25

                                                                                                        = $5.27

Number of miles covered by john and his coworkers = ([tex]5.27\div a[/tex]) miles

For more information, refer to the link given below:

https://brainly.com/question/13101306