Day 1 & 2-4.1.1 Systems of equations Defining Variables Name: I can. 4-1. Match each mathematical sentence on the right with its translation on the left. Define the variable(s). 1. 2z + 12 = 30 A. A zoo has two fewer elephants than zebras and five times more monkeys than elephants. The total number of elephants, monkeys, and 2. 12z + 5(z + 2) = 30 zebras is 30. 3. z + (z 2) + 5(z 2) = 30 B. Zola earned $30 by working two hours and receiving a $12 bonus. 4. z + 12z = 30 C. Thirty ounces of metal is created by mixing zinc with silver. The number of ounces of silver needed is twelve times the number of ounces of zinc. D. Eddie, who earns $5 per hour, worked two hours longer than Zach, who earns $12 per hour. Together they earned $30. Solve each of the 1-variable equations above using the variable you defined. For each situation, state your answer(s) in the correct units. 1. 2. 3. 4.
4-3. 1. The perimeter of a triangle is 31 cm. Sides #1 and #2 have equal length, while Side #3 is one centimeter shorter than twice the length of Side #1. Let s determine how long each side is: a) Make a sketch b) c) Write an equation that states the perimeter equal to 31 cm. d) Solve the equation. What is the length of each side? 2. A full bucket of water weighs eight kilograms. If the water weighs five times as much as the empty bucket, how much does the water weigh? 3. Find three consecutive numbers whose sum is 138. Recall Slope-intercept Form of a Linear Equation: y = mx + b Systems of equations more than one equation What the solutions look like 1 Equation every point on the line 2 or more Equations only the point(s) of intersection makes the equation TRUE. make both equations TRUE. Here it is. Found it! And another one.
4-4. Use what you know about slope-intercept form to write and solve systems of equations. The Situation - Charles and Amy are each growing a tree. Charles tree is 3 ft. tall when he plants it and is expected to grow 1.5 ft. per year. On the same day, Amy plants a tree seed. The tree from the seed is expected to grow 1.75 ft. per year. What kind of trees are they? Will the trees ever be the same size? If so, how many years will it take? Solve the problem using a table, a graph and a system of equations. Define the variables: Let x = y = Age (years) Charles Tree Amy s Tree Equations: 4-5. Models are used to represent real-life situations. They are useful for describing real-life behavior and making predictions. What did you predict about Charles and Amy s trees? Look at the graph modeling the growth of Charles and Amy s trees. What is the domain and range of Charles function? What is the domain and range of Amy s functions?
Practice: 1. Read the problem twice. The second time, highlight or underline the important information. 2. What question do you need to answer? 2. 3. Write the equations. 4. Solve the system. State your answer in the units given. 5. Does your answer make sense? 1. Herman and Jackie are saving money to pay for college. Herman currently has $15,000 and is working hard to save $1000 per month. Jackie only has $12,000 but is saving $1300 per month. In how many months will they have the same amount of savings? Write an equation for Herman s savings. Write an equation for Jackie s savings. Solve the system of equations and answer the question. Use the correct units with your answer. 2. George bought some CDs at his local store. He paid $15.95 for each CD. Nora bought the same number of CDs from a store online. She paid $13.95 for each CD, but had to pay $8 for shipping. In the end, both George and Nora spent the exact same amount of money buying their CDs! How many CDs did George buy? Write an equation modeling each situation. Solve the system of equations and answer the question..
3. Wendy is starting a catering business and is attempting to figure out who she should hire to transport the food to different locations. She has found two trucking companies. Peter s Pick Up charges $0.40 per mile and charges a flat fee of $68. Helen s Haulers charges $0.65 per mile and charges a flat fee of $23. For what distance would the cost of transporting to the produce be the same for both companies? What is that equal cost? Write a system of equations to model the situation. Solve and answer the questions. Use the correct units with your answer. Think about it: Which company charges a lower fee for a 160 mile trip? Which company will move a greater distance for $200? 4. Jonas needs a cell phone. He has a choice between two companies with the following monthly billing policies. Each company s monthly billing policy has an initial operating fee and charge per minute. Company Operating Fee Charge per Minute Terry s Telephone 29.95 0.l4 Carrie s Connections 4.95 0.39 At how many minutes is the monthly cost the same? What is the equal monthly cost of the two plans? Write a system of equations to model the situation. Solve and answer the questions. Use the correct units with your answer. Think about it: Which plan costs more 150 minutes of calls each month? Which plan provides more minutes for $ 60.00?
5. Movies-Are-Us has two video rental plans. The Regular video rental plan charges $3.25 for each video rental. The Preferred video rental plan has an $ 8.75 membership fee and charges $ 2 for each video rental. How many video rentals give the two plans the same cost? What is the equal cost? Think about it: Which video plan costs more for 18 video rentals? Which plan provides more videos for $ 30.00? 6 Katy weighs 105 pounds and is gaining 2 pounds a month. James weighs 175 pounds and is losing 3 pounds a month. When will they weigh the same amount? 7. A large pizza at Palanzio s Pizzeria costs $6.80 plus $0.90 for each topping. The cost of a large cheese pizza at Guido s Pizza is $7.30 plus $0.65 for each topping. How many toppings need to be added to a large cheese pizza from Palanzio s Pizzeria and Guido s Pizza in order for the pizzas to cost the same, not including tax? 8. Mrs. Travis wants to have a clown deliver balloons to her secretary s office. Clowns R Fun charges $1.25 per balloon and $6 delivery. Singing Balloons charges $1.95 per balloon and $2 for delivery. What is the minimum number of balloons Mrs. Travis needs to purchase in order for Clowns R Fun to have a lower price than Singing Balloons?