Each day, Lara’s mom drives her to school. On the way, she picks up three of Lara’s friends: Chan, Jason, and Marla. Each aftern
oon, she returns by the same route and drops them off at their homes. The map below is drawn to scale. It shows where each person lives and the route taken by Lara’s mom. At the end of the month, the four students agree to pay $300 in total to Lara’s mom to help pay for gasoline. They need to figure out how much each person should pay. Consider their statements below. How much should each person pay? Try to find the fairest possible method. Show all your work.
This falls under geometry. The two labeled angles are congruent, which means the line segment between them (AD in the image) is a bisector of the angle at vertex A. Use the angle bisector theorem, which says that
