Assignment 7 1. Maya. makes bead necklaces for a craft fair. It costs her $2.50 to make each necklace She needs to pay $49 for a table at the craft fair. She plans to sell each necklace for $5 Mays models her costs and revenue with the following equations: I Costs: y = 2.53: + 49 Revenue: 1; = 6:: In the equations, :2 represents the number of necklaces and y represents the amount in dollars. ' (3) Create a graph of the linear system. (b) How many necklaces must Maya. sell in order to break even? 8 '1 (c) Explain how to use the graph to determine the prot Maya will make if she sells 20 necklaces. 2. Two groups of ducks are leaving a eld and heading for a water source 50km away. The green-winged teels leave 25min before the canvaska ducks. Green-winged teals y at a. speed of 48km/h. (a) How far do the greenwinged teals y during the 25 min? Mr. de Jong Page 1 NDSS Assignment 7 Linear Systems Assignment FMP 10 (b) Canvasback ducks fly at a speed of 115km/h. The distance, d, in kilometres, travelled by each species is related to time, t, in hours, by the following equations: Green-winged teals: d = 48t + 20 Canvasback ducks: d = 115t What does t = 0 represent? Justify your answer. Then, sketch a graph of the system of linear equations. (c) Use the graph to describe the trip to the water source for the two groups of ducks. /2 Explain your reasoning. 3. The Benoit family is deciding whether to replace their conventional shower head with a low-flow model. Their current shower head uses 170L of water per 10 min shower. A typical low-flow shower head costs $25 to purchase. It uses 85L per 10 min shower. Heating the water with electricity costs approximately $0.002/L. (a) If n represents the number of 10 min showers, write an expression for the cost of n /2 showers using their current shower head. (b) Write a system of linear equations to represent the cost of showering using each 12 type of shower head. Mr. de Jong Page 2 NDSSW (o) Graph the system of linear equations. (d) What is the solution to your linear system? What does it represent? (9) How would your solution change if each shower were reduced to 8 min? Justify your answer with a graphical analysis. 4. Eunji wants to spend time at a local amusement park this summer. She is deciding which option will cost less. Option A: A season's pass costs $22, but she will have to pay $6 for parking each visit. Option B: A two-visit pass costs $16.50 and includes parking. She can buy as many passes as she wants. Represent Eunji's options using linear equations. What decision will she need to make before she can choose an option? Why? ________________ Mr. de Jong Page 3 NDSS Linear Systems Assignment FMP 10 Assignment 7 5. Two bike stores, Bikes-to-Go and Spokz, have different rental options. Spokz charges an hourly rate only. For a 5-h-long rental, both stores charge the same price. Bike Rental Options (a) How could you use the graph to determine the /1 100 hourly rate charged by Spokz? 80 Cost ($) 60 40 (b) How could the graph help you decide which op- /2 tion to choose? 20 -> Bikes-to-Go Spokz 2 6 Time (h) 6. Alex, Sandra, Christine, and Jared are hiking the Grouse Grind near Vancouver, BC. . Alex starts first. . Sandra and Christine start a short time later. They hike together at a faster speed than Alex's. . Jared starts last and hikes at the same speed as Alex. Each person travels at a constant rate. (a) Sketch a graph that shows each person's progress up the mountain. 13 Mr. de Jong Page 4 NDSSAssingIent 7 Linear Systems Assignment FM? 10 {. (b) 3111313088 systems of linear equations are created to represent the travel for each possible pair of hikers. How many solutions would each system have? Explain how the number of solutions relates to the bike. 7. A section of a local wetland habitat was damaged during a storm. A local company wishes to preserve the wetland and ensure water quality. The organizers decide to replace some of the bushes and trees. They place two orders with a nursery. 0 One order is for 40 bushes and 12 trees. It totals $1484. 0 The other order is for 25 bushes and 18 trees. It totals $1421. Create and solve a system of linear equations to determine the cost of one bush and the ' cost of one tree. ________________________-- Mr. de Jong Page 5 NDSS Assignment 7 Linear Systems Assignment FMP 10 8. Sharon washes her car at a professional carwash that participates in WaterSavers and uses 150 L per car. Her sister Bev washes her car with a hose, which uses 410 L of water. Sharon's washing machine uses 225 L of water per load. Bev has upgraded to a washing machine that uses only 95 L per load. Both sisters wash the same number of loads of laundry per week. Both wash their car once a week. (a) Develop a system of equations representing their water usage in one week. 12 (b) When their water usage is the same, how many loads of laundry does each sister do /2 in one week? Solve using elimination. (c) If each sister does four loads of laundry per week, who uses more water weekly? /2 Explain. Mr. de Jong Page 6 NDSSAssignment 7 Linear Systems Assignment FMP 10 9. The water level in a. lake is decreasing. Wildlife biologists are concerned about the silent 911 the ll population. They decide to track the number of sh in the lake. The osprey '3 3 sh-hunting bird. As part of their study, the biologists need to estimate the number of sh eaten by osprey_ Year Fish Eaten by Osprey -t_ \" -E_ I.\" the lake and the sh eaten by osprey. (3) Describe the population changes to the sh in one of sh. (13) Write a. system of linear equations to represent the populsti . (c) Solve the system of linear equations graphically. What does the point of intersection represent? (d) Predict what might eventually happen to the sh and osprey populations. Explain your thinking. ______'___#_f_" Mr. de Jong Page 7 NDSS