Write the system (2 equations) to represent the scenario. Then solve using the best method. 1.Mrs. Taylor is grading papers in the teachers' lounge. She has already finished grading 30 assignments and is grading 2 more assignments per hour. Her teaching assistant just came in to help her. He can grade at a rate of 8 assignments every hour. At some point, they will be finished and will have graded the same number of papers. How long will that take? How many papers have each graded? Show your work!!

2. A group of friends takes a day-long tubing trip down a river. Wild Rapids charges $10 to rent the tube then $2 per hour. Not Sinkin’ charges $5 to rent the tube and $3 per hour. How many hours will it take before the costs the companies are equal? Show your work!!

3. A cable television company offers two different pricing plans. Plan A charges $11.25 per month plus a one-time installation fee of $120. Plan B charges $18.75 per month plus a one-time installation fee of $60. After how many months will Pan A cost the same as Plan B? You may use technology!

4. Ms. Geyer wants to take group fitness classes at a nearby gym, but she needs to start by selecting a membership plan. With the first membership plan, Ms. Geyer can pay $40 per month, plus a $3 per class. Alternately, she can get the second membership plan and pay $20 per month plus a $4 per class. If Ms. Geyer attends a certain number of classes in a month, the two membership plans end up costing the same total amount. What is that total amount? Show your work!!

5. The Freshmen want to plan a party for June to celebrate the big accomplishment of surviving their first year. They have to decide if they are going to order pizza from Pizza Hut or Hungry Howies. Pizza Hut charges a $10 delivery fee, plus $5 for each large pizza. Alternately, Hungry Howies charges a $15 delivery fee, plus $4.50 for each large pizza. If the Freshmen buy a certain number of pizzas, the cost of choosing either company will be the same. What is the total cost and how many pizzas will they purchase? You may use technology!!

6. Compare two towing companies where the charge of a tow based on the number of miles you need to be taken.
Auto Shop towing: $15 to come pick you up, $.50 a mile for the tow.
Benny’s wrecker service: $10 to come pick you up, $.75 a mile for the tow.

After how many miles is the charge from each towing company the same? You may use technology!!

7. The Yellow Cab Company charges just $0.25 a mile, but it costs $5 to get in the cab. Express Cab charges no fee to get in the cab, but $1.50 a mile for the ride. How far must you travel until the costs for both companies are equal? You may use technology!!

8. Ashley and Emma are reading the same story for their English class. Ashley is on page 1 of the story, but she can read two pages every minute. Emma is already on page 5, but she reads one page every minute. How many minutes does it take before Ashley and Emma have read the same amount? Show your work!!