Comparing Proportional Relationships Problems

<p>Megan is looking for a part-time job. She narrows down her search to the following two positions:</p> <ul> <li>A job as a waitress, which pays a dollar amount (`d`) based on number of hours she works (`h`) as given by the equation `d = 13.25h`</li> <li>A job as pastry chef that pays the amount of `$62` for `4` hours of work.</li> </ul> <p>What are the earnings per hour for each of the positions?</p> <p> What is the difference in the hourly rate of pay between the two positions?</p>

<p>Sarah wants to buy a vacuum cleaner. She is examining the data on energy usage for Brand A and Brand B:</p><ul><li>The equation `e = 3h` represents the units of electricity, `e`, in KwH used by Brand A for `h` hours.</li><li>The table below represents the electricity usage of Brand B</li></ul><tableuiv2 data-props='{"headers":[{"type":"text","text_color":"#080808","value":"Time (`h` hours)"},{"type":"text","value":"Electricity Usage (`e` KwH)","text_color":"#080808"}],"rows":[[{"value":"`30`"},{"value":"`60`"}],[{"value":"`50`"},{"value":"`100`"}],[{"value":"`70`"},{"value":"`140`"}]]}'/> /> => </tableuiv2> <newline></newline><p>How many units of electricity per hour are used by Brand A and Brand B? </p><p> How many fewer units of electricity per hour does Brand B use than Brand A?</p>

<p>Greg, Tyron, and Erik work on the weekends delivering pizza for three different restaurants. In addition to their hourly wages, each of the restaurants offers an extra commission for each pizza that is delivered. </p><ul> <li>Greg earns his commission based on the equation `y = 1.6x`, where `y` is the money that Greg receives and `x` is the number of pizzas he has delivered.</li> <li>Erik is paid an extra `$``14` for every `8` pizzas he delivers as his commission.</li><li>The commission earned per pizza delivered by Tyron is shown by the graph below,</li></ul> <linegraph data-props='{"options":{"x_min":0,"y_min":0,"y_max":12,"x_max":12,"cell_size":20,"x_interval":1,"y_interval":1,"x_label":"Number of Pizzas","y_label":"Earnings (dollars)","title":"Tyron's Commission","x_axis_name":"x","y_axis_name":"y"},"points":[{"id":0,"x":0,"y":0,"show_point":false,"highlight_point":false,"show_coordinates":false,"show_x_intercept":false,"show_y_intercept":false,"x_coordinate_highlight":true,"y_coordinate_highlight":true,"show_x_intercept_point":false,"show_y_intercept_point":false},{"id":1,"x":2,"y":3,"show_point":true,"highlight_point":false,"highlight_point_color":"#A3A3B3","show_coordinates":true,"x_coordinate_highlight":false,"y_coordinate_highlight":true,"show_x_intercept_point":false,"show_y_intercept_point":false,"show_x_intercept":false,"show_y_intercept":false},{"id":2,"x":6,"y":9,"show_point":true,"highlight_point":true,"highlight_point_color":"#A3A3B3","show_coordinates":true,"x_coordinate_highlight":false,"y_coordinate_highlight":true,"show_x_intercept_point":false,"show_y_intercept_point":false,"show_x_intercept":false,"show_y_intercept":false},{"id":3,"x":8,"y":12,"show_point":false,"highlight_point":false,"highlight_point_color":"#A3A3B3","show_coordinates":false,"x_coordinate_highlight":false,"y_coordinate_highlight":true,"show_x_intercept_point":false,"show_y_intercept_point":false,"show_x_intercept":false,"show_y_intercept":false}],"line_segments":[{"first_point_id":0,"second_point_id":3,"show_start_arrow":false,"show_end_arrow":true,"highlight_line":"#A3A3B3"}]}'></linegraph><p>How much commission does each boy, Greg, Tyron, and Erik, get for delivering `1` pizza for their restaurant? </p><p>Which boy, Greg, Tyron, or Erik, gets the least commission for delivering `1` pizza?</p>

<p>There are two reservoirs that provide water to the city of Thirsteville. A certain volume of water, measured in cubic meters, passes through the gates of the two reservoirs each minute.</p> <ul> <li>From Reservoir A there is `49.6` cubic meters of water that pass through the gates of the reservoir in a span of `6.4` minutes.</li><li>The water release rate information for Reservoir B is shown in the below table:</li></ul> <tableuiv2 data-props='{"headers":[{"type":"text","text_color":"#080808","value":"Time (`m` minutes)"},{"type":"text","value":"Volume of Water (`v` cubic meters)","text_color":"#080808"}],"rows":[[{"value":"`5`"},{"value":"`64`"}],[{"value":"`6.25`"},{"value":"`80`"}],[{"value":"`7.5`"},{"value":"`96`"}]]}'/> /> => </tableuiv2><p>How many cubic meters of water are released from the gates of Reservoir A and Reservoir B each minute?</p><p>How much more water does Reservoir B release per minute when compared to Reservoir A?</p>

<p>Bob and Alice work for a non profit organization. Their job is to contact people and various organizations to ask for financial donations for their charity. The number of people that Bob and Alice each contact per day is shown below:<ul><li>The number of people that Alice contacts, `n`, is given by the equation: `n` = `60d`, where `d` represents the number of days that she made calls.</li><li>The information for the number of people that Bob contacts is shown by the graph:</li><ul> <LineGraph data-props='{ "options": { "x_min": 0, "y_min": 0, "y_max": 250, "x_max": 5, "cell_size": 40, "x_interval": 1, "y_interval": 50, "x_label": "Number of Days", "y_label": "Number of People", "title": "People Contacted by Bob", "x_axis_name": "x", "y_axis_name": "y" }, "points": [ { "id": 0, "x": 0, "y": 0, "show_point": false, "highlight_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "x_coordinate_highlight": true, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false }, { "id": 1, "x": 2, "y": 100, "show_point": true, "highlight_point": false, "highlight_point_color": "#A3A3B3", "show_coordinates": true, "x_coordinate_highlight": true, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_x_intercept": false, "show_y_intercept": false }, { "id": 2, "x": 3, "y": 150, "show_point": false, "highlight_point": false, "highlight_point_color": "#A3A3B3", "show_coordinates": false, "x_coordinate_highlight": true, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_x_intercept": false, "show_y_intercept": false }, { "id": 3, "x": 5, "y": 250, "show_point": false, "highlight_point": false, "highlight_point_color": "#A3A3B3", "show_coordinates": false, "x_coordinate_highlight": true, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_x_intercept": false, "show_y_intercept": false } ], "line_segments": [ { "first_point_id": 0, "second_point_id": 3, "show_start_arrow": false, "show_end_arrow": true, "highlight_line": "#000000" } ]}'></LineGraph ><p>What is the number of people contacted per day by Bob and by Alice?<p>How many more people did Alice contact in a day, compared to Bob?<p>