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Proportion Applications

Grade 7 · Ratios · Worksheet 1

  1. A recipe requires 4 cups of flour for every 3 cups of sugar. If you use 18 cups of flour, how many cups of sugar are needed? Answer: ______________
  2. Mason is drawing a scale model of a city park on a coordinate grid. The actual park is 240 meters wide and 180 meters long. On his grid, the park is drawn as a rectangle with a width of 16 units and a length of 12 units. He then draws a straight diagonal path from one corner of the rectangle to the opposite corner. If the scale of his drawing is consistent, what is the actual length of the diagonal path in meters? Round your answer to the nearest whole number. Answer: ______________
  3. Mere is making a traditional woven flax basket. The pattern requires 4 meters of flax for every 6 baskets. If Mere has 18 meters of flax, how many baskets can she make? Answer: ______________
  4. Emma is a conservationist studying elephant migration patterns. She records that a herd of elephants drinks 525 liters of water from a watering hole in 7 hours. If the herd continues drinking at the same rate, how many liters of water will they drink in 15 hours? Answer: ______________
  5. A construction company needs to mix concrete using cement, sand, and gravel in a ratio of 1:2:4. If they want to make 3500 kg of concrete, how many kilograms of sand should they use? Answer: ______________
  6. Aroha is a conservation officer tracking the migration of a herd of wildebeest. She observes that the herd travels 135 kilometers in 9 days at a steady pace. If they continue at the same rate, how many days will it take them to travel 405 kilometers? Answer: ______________
  7. A construction company needs to mix concrete using a ratio of 3 parts cement to 7 parts sand to 12 parts gravel. If they need to prepare 33,000 kg of concrete mixture, how many kilograms of sand should they use? Answer: ______________
  8. Tane is mixing concrete for a pathway. The ratio of cement to sand to gravel is 1:2:3 by volume. If Tane uses 15 buckets of gravel, how many buckets of cement and sand are needed in total? Answer: ______________
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Answer Key & Explanations

Proportion Applications · Grade 7 · Worksheet 1

  1. A recipe requires 4 cups of flour for every 3 cups of sugar. If you use 18 cups of flour, how many cups of sugar are needed? Answer: 13.5 Solution: The recipe ratio is 4 cups flour to 3 cups sugar, which can be written as 4/3. Set up a proportion where the new amount of flour is 18 cups and the unknown sugar amount is x: 4/3 = 18/x.
    Full step-by-step solution

    Step 1: The recipe ratio is 4 cups flour to 3 cups sugar, which can be written as 4/3. Step 2: Set up a proportion where the new amount of flour is 18 cups and the unknown sugar amount is x: 4/3 = 18/x. Step 3: Cross-multiply to solve for x: 4 * x = 3 * 18. Step 4: Calculate the right side: 4x = 54. Step 5: Divide both sides by 4: x = 54 / 4. Step 6: Simplify the division: x = 13.5. The answer is 13.5 cups of sugar.

  2. Mason is drawing a scale model of a city park on a coordinate grid. The actual park is 240 meters wide and 180 meters long. On his grid, the park is drawn as a rectangle with a width of 16 units and a length of 12 units. He then draws a straight diagonal path from one corner of the rectangle to the opposite corner. If the scale of his drawing is consistent, what is the actual length of the diagonal path in meters? Round your answer to the nearest whole number. Answer: 300 Solution: Find the scale factor. The actual width is 240 m and the drawn width is 16 units. So, scale factor = 240 / 16 = 15.
    Full step-by-step solution

    Step 1: Find the scale factor. The actual width is 240 m and the drawn width is 16 units. So, scale factor = 240 / 16 = 15. This means 1 unit on the drawing equals 15 meters in reality. Step 2: Find the diagonal length on the drawing. The drawn rectangle has width 16 units and length 12 units. The diagonal forms a right triangle with legs 16 and 12. Using the Pythagorean theorem: diagonal^2 = 16^2 + 12^2 = 256 + 144 = 400. So, the diagonal on the drawing = sqrt(400) = 20 units. Step 3: Convert the drawing diagonal to the actual diagonal. Actual diagonal = drawing diagonal * scale factor = 20 * 15 = 300 meters. Step 4: The actual length of the diagonal path is 300 meters.

  3. Mere is making a traditional woven flax basket. The pattern requires 4 meters of flax for every 6 baskets. If Mere has 18 meters of flax, how many baskets can she make? Answer: 27 Solution: Set up the proportion. The ratio of flax to baskets is 4 meters : 6 baskets. Let x be the number of baskets for 18 meters.
    Full step-by-step solution

    Step 1: Set up the proportion. The ratio of flax to baskets is 4 meters : 6 baskets. Let x be the number of baskets for 18 meters. So 4/6 = 18/x. Step 2: Cross-multiply: 4 * x = 6 * 18. Step 3: Simplify: 4x = 108. Step 4: Divide both sides by 4: x = 108 / 4 = 27. The answer is 27 baskets.

  4. Emma is a conservationist studying elephant migration patterns. She records that a herd of elephants drinks 525 liters of water from a watering hole in 7 hours. If the herd continues drinking at the same rate, how many liters of water will they drink in 15 hours? Answer: 1125 Solution: Set up a proportion comparing liters to hours. Let x be the number of liters in 15 hours. 525 liters / 7 hours = x liters / 15 hours Cross-multiply.
    Full step-by-step solution

    Step 1: Set up a proportion comparing liters to hours. Let x be the number of liters in 15 hours. 525 liters / 7 hours = x liters / 15 hours Step 2: Cross-multiply. 525 × 15 = 7 × x Step 3: Calculate 525 × 15. 525 × 10 = 5250 525 × 5 = 2625 5250 + 2625 = 7875 So 525 × 15 = 7875 Step 4: Write the equation. 7875 = 7x Step 5: Divide both sides by 7 to solve for x. x = 7875 ÷ 7 x = 1125 The elephants will drink 1125 liters of water in 15 hours.

  5. A construction company needs to mix concrete using cement, sand, and gravel in a ratio of 1:2:4. If they want to make 3500 kg of concrete, how many kilograms of sand should they use? Answer: 1000 Solution: The ratio of cement : sand : gravel is 1 : 2 : 4. This means for every 1 part cement, there are 2 parts sand and 4 parts gravel. Total parts = 1 + 2 + 4 = 7 parts.
    Full step-by-step solution

    Let's solve this step by step. --- **Step 1: Understand the ratio** The ratio of cement : sand : gravel is 1 : 2 : 4. This means for every 1 part cement, there are 2 parts sand and 4 parts gravel. --- **Step 2: Find the total number of parts** Total parts = 1 + 2 + 4 = 7 parts. --- **Step 3: Relate total parts to total concrete** The total concrete to be made is 3500 kg, which corresponds to 7 parts. So, 7 parts = 3500 kg. --- **Step 4: Find the weight of 1 part** 1 part = 3500 kg ÷ 7 = 500 kg. --- **Step 5: Find the weight of sand** Sand is 2 parts, so: Sand weight = 2 × 500 kg = 1000 kg. --- **Final answer:** 1000

  6. Aroha is a conservation officer tracking the migration of a herd of wildebeest. She observes that the herd travels 135 kilometers in 9 days at a steady pace. If they continue at the same rate, how many days will it take them to travel 405 kilometers? Answer: 27 Solution: Set up a proportion comparing distance to time. Let x be the number of days to travel 405 kilometers.
    Full step-by-step solution

    Step 1: Set up a proportion comparing distance to time. Let x be the number of days to travel 405 kilometers. The proportion is: 135 km / 9 days = 405 km / x days Step 2: Cross-multiply: 135 * x = 9 * 405 Step 3: Calculate 9 * 405 = 3645 Step 4: So, 135x = 3645 Step 5: Divide both sides by 135: x = 3645 / 135 Step 6: Simplify: x = 27 The answer is 27 days.

  7. A construction company needs to mix concrete using a ratio of 3 parts cement to 7 parts sand to 12 parts gravel. If they need to prepare 33,000 kg of concrete mixture, how many kilograms of sand should they use? Answer: 10500 Solution: Find the total number of parts in the ratio: 3 (cement) + 7 (sand) + 12 (gravel) = 22 total parts Determine the fraction that represents sand: 7 parts sand out of 22 total parts = 7/22 Calculate the amount of sand needed: 7/22 × 33,000 kg Perform the multiplication: (7 × 33,000) ÷ 22 = 231,000 ÷…
    Full step-by-step solution

    Step 1: Find the total number of parts in the ratio: 3 (cement) + 7 (sand) + 12 (gravel) = 22 total parts Step 2: Determine the fraction that represents sand: 7 parts sand out of 22 total parts = 7/22 Step 3: Calculate the amount of sand needed: 7/22 × 33,000 kg Step 4: Perform the multiplication: (7 × 33,000) ÷ 22 = 231,000 ÷ 22 = 10,500 Step 5: The company needs 10,500 kg of sand. The answer is 10500.

  8. Tane is mixing concrete for a pathway. The ratio of cement to sand to gravel is 1:2:3 by volume. If Tane uses 15 buckets of gravel, how many buckets of cement and sand are needed in total? Answer: 15 Solution: The ratio cement:sand:gravel = 1:2:3. Gravel is 3 parts and equals 15 buckets. Find the value of 1 part: 15 buckets ÷ 3 = 5 buckets per part.
    Full step-by-step solution

    Step 1: The ratio cement:sand:gravel = 1:2:3. Gravel is 3 parts and equals 15 buckets. Step 2: Find the value of 1 part: 15 buckets ÷ 3 = 5 buckets per part. Step 3: Cement is 1 part: 1 × 5 = 5 buckets. Step 4: Sand is 2 parts: 2 × 5 = 10 buckets. Step 5: Total buckets of cement and sand: 5 + 10 = 15 buckets. The answer is 15 buckets.