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Proportional Graphs

Grade 7 · Ratios · Worksheet 3

  1. Charlotte is filling orders for a candle company. She uses 7 kilograms of wax to make 12 candles of the same size. If Charlotte needs to make 132 candles for a large order, how many kilograms of wax will she need to use? Answer: ______________
  2. y = 15x, x = 25, y = ? Answer: ______________
  3. Liam is baking cookies for a school fundraiser. His recipe uses 2.5 cups of flour to make 15 cookies. He needs to bake enough cookies for 90 students to each get one cookie. How many cups of flour will Liam need for this batch? Answer: ______________
  4. If y = 2.75x + 8.5 and x = 24, then y = ? Answer: ______________
  5. A city is planning a new bike trail that needs to be paved. The paving company can complete 2.5 miles of trail using 15,000 pounds of asphalt. If the entire trail is 12 miles long, how many pounds of asphalt will be needed for the complete project? Answer: ______________
  6. A proportional relationship is graphed on a coordinate plane where the x-axis represents hours worked and the y-axis represents earnings in dollars. The line passes through points (0,0) and (5,87.50). If someone works for 12 hours, how much will they earn? Answer: ______________
  7. A factory produces 12500 units of a product in 8 hours. If the production rate remains constant, how many units will be produced in 36 hours? Answer: ______________
  8. A city is planning a new bike path that needs to be painted with special reflective paint. The paint company provides a graph showing that 4 gallons of paint can cover 1,200 feet of path. If the city needs to paint 15,000 feet of bike path, how many gallons of paint should they order? Answer: ______________
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Answer Key & Explanations

Proportional Graphs · Grade 7 · Worksheet 3

  1. Charlotte is filling orders for a candle company. She uses 7 kilograms of wax to make 12 candles of the same size. If Charlotte needs to make 132 candles for a large order, how many kilograms of wax will she need to use? Answer: 77 Solution: Find the amount of wax needed for one candle. 7 kilograms divided by 12 candles equals 7/12 kilograms per candle. Multiply the wax per candle by the total number of candles needed: (7/12) * 132.
    Full step-by-step solution

    Step 1: Find the amount of wax needed for one candle. 7 kilograms divided by 12 candles equals 7/12 kilograms per candle. Step 2: Multiply the wax per candle by the total number of candles needed: (7/12) * 132. Step 3: Simplify the multiplication: (7 * 132) / 12 = 924 / 12. Step 4: Divide 924 by 12 to get 77. Step 5: Charlotte will need 77 kilograms of wax to make 132 candles. The answer is 77.

  2. y = 15x, x = 25, y = ? Answer: 375 Solution: The equation is y = 15x, which is a proportional relationship with constant k = 15. Substitute x = 25 into the equation: y = 15 × 25. Multiply: 15 × 25 = 375.
    Full step-by-step solution

    Step 1: The equation is y = 15x, which is a proportional relationship with constant k = 15. Step 2: Substitute x = 25 into the equation: y = 15 × 25. Step 3: Multiply: 15 × 25 = 375. Step 4: Therefore, y = 375. The answer is 375.

  3. Liam is baking cookies for a school fundraiser. His recipe uses 2.5 cups of flour to make 15 cookies. He needs to bake enough cookies for 90 students to each get one cookie. How many cups of flour will Liam need for this batch? Answer: 15 Solution: The recipe uses 2.5 cups of flour to make 15 cookies. Liam needs 90 cookies in total. We need to find how many cups of flour are needed for 90 cookies.
    Full step-by-step solution

    Step 1: Understand the problem. The recipe uses 2.5 cups of flour to make 15 cookies. Liam needs 90 cookies in total. We need to find how many cups of flour are needed for 90 cookies. Step 2: Find how many cups per cookie. From the recipe: 15 cookies need 2.5 cups of flour. So, cups per cookie = 2.5 / 15. 2.5 / 15 = 0.1666... cups per cookie (which is 1/6 cup per cookie, but we can keep it as a decimal or fraction). Step 3: Find cups needed for 90 cookies. Multiply cups per cookie by 90: (2.5 / 15) * 90 = 2.5 * (90 / 15) = 2.5 * 6 = 15 Step 4: Conclusion. Liam needs 15 cups of flour to make 90 cookies. Answer: 15

  4. If y = 2.75x + 8.5 and x = 24, then y = ? Answer: 74.5 Solution: Start with the equation y = 2.75x + 8.5 Substitute x = 24 into the equation: y = 2.75 * 24 + 8.5 Perform the multiplication first: 2.75 * 24 = 66 Add the constant term: 66 + 8.5 = 74.5 Therefore, y = 74.5 The answer is 74.5.
    Full step-by-step solution

    Step 1: Start with the equation y = 2.75x + 8.5 Step 2: Substitute x = 24 into the equation: y = 2.75 * 24 + 8.5 Step 3: Perform the multiplication first: 2.75 * 24 = 66 Step 4: Add the constant term: 66 + 8.5 = 74.5 Step 5: Therefore, y = 74.5 The answer is 74.5.

  5. A city is planning a new bike trail that needs to be paved. The paving company can complete 2.5 miles of trail using 15,000 pounds of asphalt. If the entire trail is 12 miles long, how many pounds of asphalt will be needed for the complete project? Answer: 72000 Solution: Identify the proportional relationship: 2.5 miles requires 15,000 pounds of asphalt Find the unit rate: 15,000 ÷ 2.5 = 6,000 pounds per mile Multiply by the total trail length: 6,000 × 12 = 72,000 The total asphalt needed is 72,000 pounds
    Full step-by-step solution

    Step 1: Identify the proportional relationship: 2.5 miles requires 15,000 pounds of asphalt Step 2: Find the unit rate: 15,000 ÷ 2.5 = 6,000 pounds per mile Step 3: Multiply by the total trail length: 6,000 × 12 = 72,000 Step 4: The total asphalt needed is 72,000 pounds

  6. A proportional relationship is graphed on a coordinate plane where the x-axis represents hours worked and the y-axis represents earnings in dollars. The line passes through points (0,0) and (5,87.50). If someone works for 12 hours, how much will they earn? Answer: 210 Solution: Find the constant of proportionality (earnings per hour) using the given points (0,0) and (5,87.50). Calculate the rate: 87.50 ÷ 5 = 17.50 dollars per hour. Apply this rate to 12 hours: 12 × 17.50 = 210 dollars.
    Full step-by-step solution

    Step 1: Find the constant of proportionality (earnings per hour) using the given points (0,0) and (5,87.50). Step 2: Calculate the rate: 87.50 ÷ 5 = 17.50 dollars per hour. Step 3: Apply this rate to 12 hours: 12 × 17.50 = 210 dollars. Step 4: The earnings for 12 hours of work is 210 dollars.

  7. A factory produces 12500 units of a product in 8 hours. If the production rate remains constant, how many units will be produced in 36 hours? Answer: 56250 Solution: We know that in 8 hours, the factory produces 12500 units. We want to find how many units are produced in 36 hours, assuming the production rate is constant.
    Full step-by-step solution

    Step 1: Understand the problem We know that in 8 hours, the factory produces 12500 units. We want to find how many units are produced in 36 hours, assuming the production rate is constant. Step 2: Find the production rate per hour Production rate = Total units / Total hours Rate = 12500 units / 8 hours Rate = 1562.5 units per hour Step 3: Calculate units produced in 36 hours Units in 36 hours = Rate × 36 Units = 1562.5 × 36 Step 4: Perform the multiplication First, 1562.5 × 30 = 46875 Then, 1562.5 × 6 = 9375 Add them: 46875 + 9375 = 56250 Step 5: Conclusion At a constant rate, the factory will produce 56250 units in 36 hours. Final answer: 56250

  8. A city is planning a new bike path that needs to be painted with special reflective paint. The paint company provides a graph showing that 4 gallons of paint can cover 1,200 feet of path. If the city needs to paint 15,000 feet of bike path, how many gallons of paint should they order? Answer: 50 Solution: Identify the proportional relationship from the graph: 4 gallons covers 1,200 feet. Find the coverage rate per gallon: 1,200 feet ÷ 4 gallons = 300 feet per gallon.
    Full step-by-step solution

    Step 1: Identify the proportional relationship from the graph: 4 gallons covers 1,200 feet. Step 2: Find the coverage rate per gallon: 1,200 feet ÷ 4 gallons = 300 feet per gallon. Step 3: Calculate gallons needed for 15,000 feet: 15,000 feet ÷ 300 feet/gallon = 50 gallons. The answer is 50.