7th Grade Math Rates And Proportional Relationships Unit Test

<p>A conveyor belt at a website fulfillment plant moves a package `205.5` meters in `1 1/4` hours. </p><p>Assuming the conveyor belt does not stop and is moving at a constant rate, how many meters will the package move in `1` hour?</br><highlight data-color="#666" data-style="italic">Write your answer as an exact decimal or simplified fraction/mixed number.</highlight></p>

<p>It took Janice `7.5` minutes to spray fertilizer over `34.5` square yards of her garden. At this rate, how much of her garden will she spray with fertilizer in `1` hour? </p>

<p>Margo and Dave are taking a typing class as an elective. Margo can type `1/4` page of a document in `10` minutes, while it takes Dave `20` minutes to type `1/4` of a page. </p><p>What is the difference in their typing speeds in pages per hour?</br><highlight data-color="#666" data-style="italic">Write your answer as an exact decimal or simplified fraction/mixed number.</highlight></p>

<p>Emily and Seth are both designing flags for the school gala. Emily uses `4 1/2` feet of fabric for `9` flags while Seth uses `2 1/4` feet of fabric for `3` flags.</p><p>What is the difference in the average length of fabric used per flag by Emily and Seth? </br><highlight data-color="#666" data-style="italic">Write your answer as an exact decimal or simplified fraction/mixed number.</highlight></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>Does the graph represent a proportional relationship? </p><selectivedisplay data-props='{"show_in_create":true, "show_in_problem_qa": true}'><LineGraph data-props='{ "options": { "x_min": -3, "y_min": -3, "y_max": 3, "x_max": 3, "cell_size": 20, "x_interval": 0.5, "y_interval": 0.5, "show_major_and_minor_grid_lines": true, "x_skip_interval": 1, "y_skip_interval": 1 }, "points": [ { "id": 0, "x": 0, "y": 1.5, "show_point": false, "highlight_point": false, "highlight_point_color": "#377CF6", "point_shape": "line", "x_coordinate_highlight": true, "y_coordinate_highlight": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "show_x_intercept_point": false, "show_y_intercept_point": false }, { "id": 1, "x": 2.5, "y": 3, "show_point": false, "highlight_point": true, "highlight_point_color": "black", "point_shape": "line", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "show_x_intercept_point": false, "show_y_intercept_point": false } ], "line_segments": [ { "first_point_id": 0, "second_point_id": 1, "show_start_arrow": false, "show_end_arrow": true, "start_arrow_shape": " ", "end_arrow_shape": " ", "highlight_line": "black", "label": " " } ]}'></LineGraph >

<p>Find the distance covered per hour in each row of the table. Use that to determine if the table represents a proportional relationship between the time spent walking and the distance covered.</p><p><tableuiv2 data-props='{"headers":[{"type":"text","text_color":"#080808","value":"Time (hours)"},{"type":"text","value":"Distance (miles)","text_color":"#080808"}],"rows":[[{"value":"`2`"},{"value":"`3`"}],[{"value":"`5`"},{"value":"`10`"}],[{"value":"`6`"},{"value":"`15`"}]]}'/></tableuiv2></p><highlight data-color="#666" data-style="italic">Write each answer as a whole number or exact decimal.</highlight></p>

<p>In Pizza Shop, `6` veggie pizzas cost `$75` and `8` bacon pizzas cost `$100`. </p><ul><li>Find the cost for each pizza.</li><li>Use that to determine if there is a proportional relationship between the number of pizzas and the total cost.</li></ul><highlight data-color="#666" data-style="italic">Write your answer as an exact decimal or simplified fraction/mixed number.</highlight></p>

<p>Solve for k.</p><p>`(1 3/4)/k=(2 1/3)/6`</p>

<p>Solve for k.</p><p>`(1/2)/k=(2/3)/6`</p>

<p>James is recording the time needed to fill oil barrels using a pipe of a certain radius. He notes down that `4` oil barrels were filled by the pipe in `1/3` hour. At this rate, how long will it take to fill `18` more oil barrels using the same pipe? </br><highlight data-color="#666" data-style="italic">Write your answer as an exact decimal or simplified fraction/mixed number. </highlight></p>

<p>Mateo is participating in a bike-a-thon to raise money for new band uniforms at his school. He will earn `$3` in pledge money for every `6` miles that he rides his bike.</p> <li>How much money will Mateo earn for riding his bike for `1` mile?</li> <li>How many miles must Mateo ride his bike to earn `1` dollar?</li><highlight data-color="#666" data-style="italic">Write each answer as whole number, exact decimal, or simplified fraction/mixed number.</highlight>

<p>The point (`1/3`, `4/5`) lies on the graph of a proportional relationship. Find two other points that would also be on the graph.</p> <ul><li>The first point should represent the unit rate. </li><li>The second point can be any other point besides the origin.</li></ul>

<p>Write the constant of proportionality (`k`) for the equation: </p><p> `y = 49/8x`</p>

<p>Yesterday, there was a steady rainfall throughout the day. The table below shows that the amount of rainfall yesterday was directly proportional to the number of hours that it rained. </p><p>What is the constant of proportionality (`k`) between the amount of rainfall (`r` `mm`) and the number of hours that it rained (`h` hours)?</p> <tableuiv2 data-props='{"headers":[{"type":"text","text_color":"#080808","value":" Rainfall time (`h` hours)"},{"type":"text","value":"Amount of Rain (`r` `mm`)","text_color":"#080808"}],"rows":[[{"value":"`2.2`"},{"value":"`19.8`"}],[{"value":"`3.3`"},{"value":"`29.7`"}],[{"value":"`5.5`"},{"value":"`49.5`"}]]}'/>

<p>Charlotte works at Central Perk coffee shop. During the morning rush at the drive-thru line, she can serve `45` cups of coffee in `3/4` of an hour. The number of cups of coffee that Charlotte can serve is directly proportional to the amount of time that she works. </p><p>What is the constant of proportionality (`k`) between the amount of time that she works (`t` hours) and the number of cups of coffee Charlotte serves (`c`) ?</p>

<p>The following table shows a proportional relationship between the weight of lemon candies, in pounds, that were purchased and the cost, in dollars, of the candies. </p><tableuiv2 data-props='{"headers":[{"type":"text","text_color":"#080808","value":"Weight of Candy (`x` pounds) "},{"type":"text","value":"Cost (`y` dollars)","text_color":"#080808"}],"rows":[[{"value":"`2/3`"},{"value":"`14`"}],[{"value":"`4/3`"},{"value":"`28`"}],[{"value":"`8/3`"},{"value":"`56`"}]]}'/> /> => </tableuiv2><p>Write an equation to describe the relationship between the weight of the lemon candies that were purchased (`x`) and the total cost (`y`). </p>

<p>A glass factory produces `28` bottles in `8` minutes. The number of bottles produced is directly proportional to the amount of production time in minutes. </p><p>Write an equation that shows the relationship between the amount of production time (`x` minutes) and the number of bottles that are produced (`y`).</p>

<p>Jamie is looking at the blueprint of her new apartment. The dimensions of the rectangular main living area are shown in the drawing below. The scale factor used in the blueprint is `1` inch`=3` feet.</p><Rectangle data-props='{ "height": 6, "width": 8, "unit": "in", "height_label": "", "width_label": "", "left": { "label": "6 in", "highlight": false, "color": "" }, "right": { "label": "", "highlight": false, "color": "" }, "top": { "label": "", "highlight": false, "color": "" }, "bottom": { "label": "8 in", "highlight": false, "color": "" }, "fill": "#F2F2F6", "outline": "#000"}'></Rectangle ><p>What is the length, width and perimeter of the actual living area?</p>

<p>A large map at a rest stop on a major highway in the state of New York shows the distance between Syracuse and Albany as being `32` inches. The scale on the map is `1` inch = `4.5` miles. </p><p>How far apart are the two cities in real life?</p>