Applications of Linear Systems Page | 1

  1. Scientists studied the weights of two alligators over a period of 12 months. The initial weight and growth rate of each alligator are shown below. After how many months did the alligator weigh the same amount?

Alligator 1

Initial Weight: 4lb

Rate of Growth: 1.5 lbs per month

Alligator 2

Initial Weight: 6 lb.

Rate of Growth: 1 lb per month

  1. Tickets for a concert cost $10 each if you order them online, but you must pay a service charge of $8 per order. The tickets are $12 each if you buy them at the door on the night of the concert.

a. Write a system of equations to model the situation.

b. Graph the equations and find the intersection point. What does this point represent?

  1. The number of right-handed students in a mathematics class is nine times the number of left- handed students. The total number of students in the class is 30. How many right-handed students are in the class? How many left-handed students are in your class?
  1. A plant nursery is growing a tree that is 3 ft tall and grows at an average rate of 1 ft per year. Another tree at the nursery is 4 ft tall and grows at an average rate of 0.5 ft per year. After how many years will the trees be the same height?
  1. At a local fitness center, members pay a $20 membership fee and $3 for each aerobics class. Nonmembers pay $5 for each aerobics class. For what number of aerobics classes will the cost for members and nonmembers be the same?
  1. You are looking for an after school job. One job pays $9 per hour. Another pays $12 per hour, but you must buy a uniform that costs $39. After how many hours of work would your net earnings from either job be the same?
  1. Two hikers are walking along a marked trail. The first hiker starts at a point 6 miles from the beginning of the trail and walks at a speed of 4 miles per hour. At the same time, the second hiker starts 1 mile from the beginning and walks at a speed of 3 miles per hour.
  2. What is a system of equations that models the situation?
  3. Graph the two equations and find the intersection point.
  4. Is the intersection point meaningful in this situation? Explain.
  1. A cell phone provider offers a plan that costs $40 per month plus $.20 per text message sent or received. A comparable plan costs $60 per month but offers unlimited text messaging.
  2. How many text messages would you have to send or receive in order for the plans to cost the same each month?
  3. If you send or receive an average of 50 test messages each month, which plan would you choose? Why?
  1. The costs for parking in two different parking garages are given in the table.

Garage Parking Fees
A / $5 / $2.50
B / $20 / $0
  1. What is a system of equations that models the situation?
  2. How many hours of parking would cost the same parking in either garage?
  3. If you needed to park a car for 3 hours, which garage would you choose? Why?
  1. A snack bar sells two sizes of snack packs. A large snack pack is $5, and a small snack pack is $3. In one day, the snack bar sold 60 snack packs for a total of $220. How many small snack packs did the snack bar sell?
  1. Adult tickets to a play cost $22. Tickets for children cost $15. Tickets for a group of 11 people cost a total of $228. Write and solve a system of equations to find how many children and how many adults were in the group.
  1. A school is planning a field trip for 142 people. The trip will use six drivers and two types of vehicles: buses and vans. A bus can seat 51 passengers. A van can seat 10 passengers. Write and solve a system of equations to find how many buses and how many vans will be needed.
  1. You have $3.70 in dimes and quarters. You have 5 more quarters than dimes. How many of each type of coin do you have?
  1. An artist is going to sell two sizes of prints at an art fair. The artist will charge $20 for a small print and $45 for a large print. The artist would like to sell twice as many small prints as large prints. The booth the artist is renting for the day costs $510. How many of each size print must the artist sell in order to break even at the fair?
  1. At a certain high school, 350 students are taking an algebra course. The ratio of boys to girls taking algebra is 33:37. How many more girls are taking algebra than boys?
  1. A pyro technician plans for two fireworks to explode together at the same height in the air. Firework A travels at a speed of 220 ft/s and Firework B travels at a speed of 200 ft/s. Firework B is launched .25 seconds before Firework A. How many seconds after Firework B launches will both fireworks explode?
  1. You are making blueberry muffins and need to buy a muffin tin and baking cups. Each package of baking cups has 50 baking cups and costs $1.25. The muffin tin costs $15. If you have $22 to spend, at most how many baking cups can you buy?
  1. The theater club sells a total of 101 tickets to its first play. A student ticket costs $1. An adult ticket costs $2.50. Total ticket sales are $164. How many student tickets were sold?
  1. Your school’s talent show will feature 12 solo acts and 2 ensemble acts. The show will last 90 minutes. The 6 solo performers judged best will give a repeat performance at a second 60-minute show, which will also feature the 2 ensembles acts. Each solo act lasts x minutes, and each ensemble act lasts y minutes. How long is each solo act? How long is each ensemble act?
  1. A toy store worker packed two boxes of identical dolls and plush toys for shipping in boxes that weigh 1 oz when empty. One box held 3 dolls and 4 plush toys. The worker marked the weight as 12 oz. The other box held 2 dolls and 3 plush toys. The worker marked the weight as 10 oz. Explain why the worker must have made a mistake.
  1. Half a pepperoni pizza plus three fourths of a ham-and-pineapple pizza contains 765 Calories. One fourth of a pepperoni pizza plus a whole ham-and-pineapple pizza contains 745 Calories. How many Calories are in a whole pepperoni pizza? How many Calories are in a whole ham-and-pineapple pizza?
  1. A hotel offers two activity packages. One costs $192 and includes 3 hours of horseback riding and 2 hours of parasailing. The second costs $213 and includes 2 hours of horseback riding and 3 hours of parasailing. What is the cost for 1 hour of each activity?