Word Problems ECA Review Andrei and his younger

Word Problems ECA Review

• Andrei and his younger brother are having a race. Because the younger brother can’t run as fast, Andrei lets him start out 5 m ahead. Andrei runs at a speed of 7. 7 m/s. His younger brother runs at 6. 5 m/s. The total length of the race is 50 m. • Write an equation to find how long it will take Andrei to finish the race. Solve the equation to find the time. 50 m = 7. 7 m/s * t t = 6. 49 sec 1 Linear Equations

• Write an equation to find how long it will take Andrei’s younger brother to finish the race. Solve the equation to find the time. 50 m – 5 m = 6. 5 m/s * t t = 6. 92 sec 1 Linear Equations

• Who wins the race? How far ahead was the winner at the time he crossed the finish line? Andrei (6. 92 sec - 6. 49 sec) * 6. 5 m/s = 2. 8 m 1 Linear Equations

• Amber makes $6 an hour at a sandwich shop. She wants to know how many hours she needs to work to save $500 in her bank account. On her first paycheck, she notices that her net pay is about 75% of her gross pay. • How many hours must she work to earn $500 in gross pay? $500 / 6 ($/hr) = 83. 3 hours 2 Solving

• How many hours must she work to earn $500 in net pay? ($500 / 0. 75) / 6 ($/hr) = 111. 1 hours 2 Solving

• Harold cuts lawns after school. He has a problem on Wednesdays when he cuts Mr. Fleming’s lawn. His lawn mower has two speeds—at the higher speed he can get the job done quickly, but he always runs out of gas; at the lower speed he has plenty of gas, but it seems to take forever to get the job done. So he has collected this information. • On Monday he cut a 15 -meter-by-12 -meter lawn at the higher speed in 18 minutes. He used a half tank of gas, or 0. 6 liter. • On Tuesday he cut a 20 -meter-by-14 -meter lawn at the lower speed in 40 minutes. He used a half tank of gas. • Mr. Fleming’s lawn measures 22 meters by 18 meters. 3 Systems

• How many square meters of lawn can Harold cut per minute at the higher speed? (15 m * 12 m) / 18 min = 10 m 2/min • At the lower speed? (20 m * 14 m) / 40 min = 7 m 2/min 3 Systems

• If Harold decides to cut Mr. Fleming’s lawn using the higher speed for 10 minutes and the lower speed for 8 minutes, will he finish the job? 10 min * 10 m 2/min + 8 min * 7 m 2/min = 156 m 2 Mr. Flemings Lawn = 22 m * 18 m = 396 m 2 Harold will not finish the job. We need a better method to split up the time 3 Systems

• Let h represent the number of minutes cutting at higher speed, and let l represent the number of minutes cutting at lower speed. • Write an equation that models completion of Mr. Fleming’s lawn. h * 10 + l * 7 = 396 3 Systems

• How much gas does the lawn mower use in liters per minute at the higher speed? 0. 6 l/18 min = 1/30 l/min • At the lower speed? 0. 6 l/40 min = 3/200 l/min 3 Systems

• Write an equation in terms of h and l that has Harold use all of his gas. h * 10 + l * 7 = 396 Equation based on speed h * 1/30 + l * 3/200 = 1. 2 Equation based on gas 10 * h + 7 * l = 396 20 * h + 9 * l = 720 Rewrite first equation Rewrite second equation Solution l = 14. 4, h = 29. 52 3 Systems

• Give a real-world meaning of the solution. Run at low speed for 14. 4 minutes and high speed for 29. 52 minutes to cut the grass the fastest way without having to stop and refill the gas. 3 Systems

• The Creekside Theater is putting on a play. The Hanson family bought five adult tickets and three child tickets for $131. 25. The Rivera family bought three adult tickets and four child tickets for $106. 25. • Write a system of equations to represent this situation. 4 Systems

• How much does an adult ticket cost? $18. 75 • How much does a child ticket cost? 4 Systems $12. 50

• The function f (x)=0. 0015 x(150 – x) models the rate at which the population of fish grows in a large aquarium. The x-value is the number of fish, and the f (x)-value is the rate of increase in the number of fish per week. • Find f (60), and give a real-world meaning for this value. When there are 60 fish in the tank, the population is growing at a rate of about 8 fish per week. 5 Quadratics

• For what values of x does f (x)=0? • What do these values represent? When there are no fish or 150 fish, the population does not grow. 5 Quadratics

• How many fish are there when the population is growing fastest? The maximum growth rate corresponds to the vertex. The x-coordinate of the vertex is 75, the number halfway between the x-intercepts. There are 75 fish when the population is growing fastest. 5 Quadratics

• What is the maximum number of fish the aquarium has to support? The population no longer grows once there are 150 fish, so this is the maximum number of fish the tank has to support. 5 Quadratics

• Graph this function. 5 Quadratics

• A recent catalog price for tennis balls was $4. 25 for a can with three balls. The shipping charge per order was $1. 00. • Write an equation that you can use to project the costs for ordering different numbers of cans. y = 4. 25 x + 1. 00 6 Functions

• Draw a graph showing this relationship. 6 Functions

• How does raising the shipping charge by 50¢ affect the graph? It shifts the graph up 0. 50 unit on the y-axis. 6 Functions