Scouting for Prizes! Modeling Linear Inequalities. Lesson 2.3 Assignment

Transcription

1 Lesson.3 Assignment Scouting for Prizes! Modeling Linear Inequalities Chang-Ho is going on a trip to visit some friends from summer camp. He will use $40 for food and entertainment. He will also need money to cover the cost of gas. The price of gas at the time of his trip is $3.5 per gallon. 1. Consider a function in the form C(g) to represent this problem situation. a. Write a function to represent the total cost of the trip as a function of the number of gallons used. b. Identify the independent and dependent quantities and their units. c. Identify the rate of change and the y-intercept. Explain their meanings in terms of the problem situation. d. Graph the function representing this situation on the coordinate plane. y Total Cost of Trip (dollars) Amount of Gas (gallons) x Chapter Assignments 3

2 Lesson.3 Assignment page e. Use the graph to determine how many gallons of gas Chang-Ho can buy if he has $170 saved for the trip. Draw an oval on the graph to represent the solution. Then write your answer in words and as an inequality. f. Verify the solution set you interpreted from the graph. g. Chang-Ho s mom gives him some money for his trip. He now has a total of $0 saved for the trip. What is the greatest number of gallons of gas he can buy before he runs out of money? Show your work and graph your solution on the number line. 4 Chapter Assignments

3 Lesson.3 Assignment page 3 h. If Chang-Ho spent more than $9 on his trip, how much gas could he have bought? Show your work and graph your solution on the number line. Chang-Ho is on his way to visit his friends at camp. Halfway to his destination, he realizes there is a slow leak in one of the tires. He checks the pressure and it is at 6 psi. It appears to be losing 0.1 psi per minute.. Write a function, p(t), to show the tire s pressure as a function of time in minutes. 3. Chang-Ho knows that if the pressure in the tire goes below psi it may cause a tire blowout. What is the greatest amount of time that he can drive before the tire pressure hits psi? Show your work and graph the solution Time (minutes) Chapter Assignments 5

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5 Lesson.4 Assignment We re Shipping Out! Solving and Graphing Compound Inequalities 1. Taneisha s family has signed up for a new cell phone plan. Taneisha now has a limit on the number of texts she can send or receive each month. She can text no more than 300 times per month. a. What is the least number of texts she can make in a month? b. Write an inequality to represent the statement. Use n for the number of texts. c. What is the greatest number of texts she can make in a month? d. Write an inequality to represent the statement. Use n for the number of texts. e. Write the statements from parts (b) and (d) as a compound inequality. f. Write the compound inequality in compact form. g. Graph the inequality. Describe your number line representation. Chapter Assignments 7

6 Lesson.4 Assignment page. Taneisha s family s new cell phone plan costs $55 per month plus $0.0 for each text with a maximum of 300 texts per month. Let t represent the number of texts made during the month. a. Write an expression to represent the total monthly cost of the plan. b. Determine the minimum cost per month by using the least number of texts Taneisha can make in a month. c. Write an inequality to represent the statement. Use c for the monthly cost. d. Determine the maximum cost per month by using the greatest number of texts Taneisha can make in a month. e. Write an inequality to represent the statement. Use c for the monthly cost. f. Write the compound inequality that represents the cost of the plan. g. Write the compound inequality in compact form. h. Graph the inequality. Describe your number line representation. 8 Chapter Assignments

7 Lesson.4 Assignment page 3 3. John owns a 50-acre apple orchard. Among his many concerns during the growing season is the amount of rainfall. Unfavorable conditions such as drought and flooding will affect tree production. John does not want rainfall amounts to be less than 10 inches or more than 50 inches. a. Represent the undesirable rainfall amounts on the number line. b. Write a compound inequality to represent the same information. Define your variable. 4. At John s apple orchard, the profit he will make depends on the number of bushels he grows and sells. He makes $5 per bushel but must subtract $300,000 for costs associated with growing the trees in order to calculate his profit. a. Write an expression to represent the profit John will make. Let b represent the number of bushels he will produce and sell. b. John must make at least $80,000 to pay the bills, but he does not want to make more than $50,000 because it will put him in a higher tax bracket. Write a compound inequality that represents the amount of profit John can make. c. Solve the compound inequality. Show your work. d. Graph the solution to the compound inequality. Describe the solution region in terms of the problem situation. Chapter Assignments 9