Systems of Equations Graphing EE.8

Line Q passes through the points (-2, -10) and (3, 5). Line R passes through the points (-1, 5) and (3, 1). At what point do the two lines intersect?

Franco flew home from vacation with a heavy bag. With the first airline he flew, Franco had to pay $30 to check his bag, plus $5 for every kilogram that his bag was over the weight limit. The next flight was with another airline that had the same weight limit. Franco had to pay $10 per kilogram that his bag was over the weight limit, in addition to the checked bag fee of $15. By coincidence, the fees ended up being the same with both airlines. How large was each airline's fee?

The McClure family is looking to rent a large truck for their upcoming move. With Sophie's Moving, they would pay $10 for the first day plus $8 per additional day. With Westford Rent-a-Truck, in comparison, the family would pay $20 for the first day plus $7 per additional day. Before deciding on which company to use, Mrs. McClure wants to find out what number of additional days would make the two choices equivalent with regards to cost. What would the total cost be?

Dakota has punch cards for her favorite tea house and her favorite coffee shop. She currently has 2 punches on the tea punch card and 4 punches on the coffee punch card. Given her regular routine, she consistently earns 4 new punches per week on the tea punch card and 3 on the coffee punch card. Before too long, Dakota will have the same number of punches on each card. How long will that take?

A pair of kids and a pair of adults decided to compete in a three-legged race. The kids got to start 10 meters ahead of the adults, since they had shorter legs. When they were told to start, the kids hobbled forward at a rate of 3 meters per second, and the adults hobbled after them at a rate of 4 meters per second. Soon they were side-by-side. How far did the adults go?