Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Proportional relationships can be identified in both tables and graphs. Today you will have an opportunity to take a closer look at how graphs and tables for proportional relationships can help you organize your work to find any missing value quickly and easily. 4-46. Robert’s new hybrid car has a gas tank that holds 12 gallons of gas. When the tank is full, he can drive 420 miles. Assume that his car uses gas at a steady rate. A. Is the relationship between the number of gallons of gas used and the number of miles that can be driven proportional? For example, does it change like Sonja’s birdseed prediction, or is it more like Gustavo’s college savings? Explain how you know. B. Show how much gas Robert’s car will use at various distances by copying and completing the table below. A. Robert decided to graph the situation, as shown below. The distance Robert can travel using one gallon of gas is called the unit rate. Use Robert’s graph to predict how far he can drive using one gallon of gas. That is, find his unit rate. B. While a graph is a useful tool for estimating, it is often difficult to find an exact answer on a graph. What is significant about the point labeled (1, y)? How can you calculate y? C. Use the table in part (b) and your result in part (d) to find Robert’s unit rate. D. Work with your team to write the equation to find the exact number of miles Robert can drive with any number of gallons of gas. Be prepared to share your strategy. E. Use your equation to find out how many gallons of gas Robert will need to drive 287 miles. . 4-47. THE YOGURT SHOP Jell E. Bean owns the local frozen yogurt shop. At her store, customers serve themselves a bowl of frozen yogurt and top it with chocolate chips, frozen raspberries, and any of the different treats available. Customers must then weigh their creations and are charged by the weight of their bowls. Jell E. Bean charges $32 for five pounds of dessert, but not many people buy that much frozen yogurt. She needs you to help her figure out how much to charge her customers. She has customers that are young children who buy only a small amount of yogurt as well as large groups that come in and pay for everyone’s yogurt together. A. Is it reasonable to assume that the weight of the yogurt is proportional to its cost? How can you tell? B. Assuming it is proportional, make a table that lists the price for at least ten different weights of yogurt. Be sure to include at least three weights that are not whole numbers. C. What is the unit rate of the yogurt? (Stores often call this the unit price.) Use the unit rate to write an equation that Jell E. Bean can use to calculate the amount any customer will pay. D. If Jell E. Bean decided to start charging $0.50 for each cup before her customers started filling it with yogurt and toppings, could you use the same equation to find the new prices? Why or why not? 4-48. Lexie claims that she can send 14 text messages in 22 minutes. Her teammates Kenny and Esther are trying to predict how many text messages Lexie can send in a 55-minute lunch period if she keeps going at the same rate. a. Is the relationship between the number of text messages and time in minutes proportional? Why or why not? b. Kenny represented the situation using the table shown below. Explain Kenny’s strategy for using the table. i. c. Esther wants to solve the problem using an equation. Help her write an equation to determine how many text messages Lexie could send in any number of minutes. d. Find the missing value in Kenny’s table. e. Solve Esther’s equation. Will she get the same answer as Kenny? f. What is Lexie’s unit rate? That is, how many text messages can she send in 1 minute? 4-49. Additional Challenge: Use your reasoning skills to compute each unit rate (the price per pound). A. $4.20 for pound of cheese B. $1.50 for pound of bananas C. $6.00 for pound of deli roast beef D. $7.50 for pound of sliced turkey Proportional Relationships A relationship is proportional if one quantity is a multiple of the other. This relationship can be identified in tables, graphs, and equations. Table: Equivalent ratios of (or ) can be seen in a table. Graph: A straight line through the origin. Equation: An equation of the form y = kx where k is the constant of proportionality. Example: Three pounds of chicken costs $7.00. What is the cost for x pounds? Equation: The relationship between pounds and cost is proportional. The table has equivalent ratios ( ), the graph is a straight line through the origin, and the equation is of the form y = kx. Example: The county fair costs $5.00 to enter and $1.00 per ride. Equation: y = 1x + 5 The relationship between rides and cost is not proportional, because the table does not contain equivalent ratios ( addition. ), the graph does not pass through the origin, and the equation contains