Proportion Applications

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Proportion Applications · Grade 7 · Worksheet 2

1. Tane is a farmer who wants to fertilize his field. He knows that 12 bags of fertilizer can cover 450 square meters of land. If his field is 1,350 square meters, how many bags of fertilizer will he need to buy to cover the entire field? Answer: 36 Solution: Write the proportion as bags per area: 12 bags / 450 sq m = x bags / 1350 sq m. Cross-multiply: 12 * 1350 = 450 * x. Calculate 12 * 1350 = 16200.
   Full step-by-step solution

   Step 1: Write the proportion as bags per area: 12 bags / 450 sq m = x bags / 1350 sq m. Step 2: Cross-multiply: 12 * 1350 = 450 * x. Step 3: Calculate 12 * 1350 = 16200. Step 4: So 16200 = 450x. Step 5: Divide both sides by 450: x = 16200 / 450. Step 6: 16200 / 450 = 36. Therefore, Tane needs 36 bags of fertilizer.

2. Emma is creating a scale drawing of a rectangular playground on a coordinate grid. The playground's actual dimensions are 35 meters by 21 meters. On her drawing, the length is represented by the segment from (0, 0) to (25, 0). Using the same scale, what should be the length of the segment representing the width from (0, 0) to (0, y)? Answer: 15 Solution: The actual length is 35 m, and the drawing length is 25 units. Simplify the ratio: 25/35 = 5/7. This means every 5 units on the drawing represents 7 m in reality.
   Full step-by-step solution

   Step 1: The actual length is 35 m, and the drawing length is 25 units. So the scale ratio is drawing length / actual length = 25 / 35. Step 2: Simplify the ratio: 25/35 = 5/7. This means every 5 units on the drawing represents 7 m in reality. Step 3: The actual width is 21 m. Let y be the drawing width in units. Set up the proportion: y / 21 = 5 / 7. Step 4: Cross-multiply: 7 * y = 5 * 21. Step 5: 7y = 105. Step 6: Divide both sides by 7: y = 15. Step 7: The width segment should be 15 units long. The answer is 15.

3. A car travels 240 km on 15 liters of fuel. How many liters are needed for a 400 km trip? Answer: 25 Solution: Set up the proportion based on the given information: 240 km / 15 liters = 400 km / x liters. Write the proportion as an equation: 240/15 = 400/x. Cross-multiply to solve for x: 240 * x = 15 * 400.
   Full step-by-step solution

   Step 1: Set up the proportion based on the given information: 240 km / 15 liters = 400 km / x liters. Step 2: Write the proportion as an equation: 240/15 = 400/x. Step 3: Cross-multiply to solve for x: 240 * x = 15 * 400. Step 4: Calculate the right side: 15 * 400 = 6000. Step 5: The equation is now 240x = 6000. Step 6: Divide both sides by 240 to solve for x: x = 6000 / 240. Step 7: Calculate the division: 6000 ÷ 240 = 25. The answer is 25 liters.

4. A construction company needs to mix concrete using a ratio of 3 parts cement to 5 parts sand to 2 parts gravel. If they want to make 2500 kilograms of concrete mixture, how many kilograms of sand should they use? Answer: 1250 Solution: The ratio of cement : sand : gravel is 3 : 5 : 2. This means for every 3 parts cement, there are 5 parts sand and 2 parts gravel. Total parts = 3 + 5 + 2 = 10 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 3 : 5 : 2. This means for every 3 parts cement, there are 5 parts sand and 2 parts gravel. Step 2: Find the total number of parts Total parts = 3 + 5 + 2 = 10 parts. Step 3: Relate parts to the total mixture weight We want 2500 kg of concrete in total. So, 10 parts = 2500 kg. Step 4: Find the weight of 1 part 1 part = 2500 kg / 10 = 250 kg. Step 5: Find the weight of sand Sand is 5 parts, so: Sand weight = 5 × 250 kg = 1250 kg. Step 6: Conclusion They need 1250 kg of sand. Final answer: 1250

5. Liam is mixing paint for an art project. He needs to create a specific shade of purple by mixing red and blue paint in a 5:7 ratio. If Liam uses 350 milliliters of red paint, how many milliliters of blue paint should he add to maintain the correct ratio? Answer: 490 Solution: We are told that the ratio of red paint to blue paint is 5:7. This means for every 5 parts of red paint, we need 7 parts of blue paint. Let the amount of red paint be 5 units and the amount of blue paint be 7 units.
   Full step-by-step solution

   We are told that the ratio of red paint to blue paint is 5:7. This means for every 5 parts of red paint, we need 7 parts of blue paint. Step 1: Understand the ratio relationship. Let the amount of red paint be 5 units and the amount of blue paint be 7 units. We know Liam uses 350 milliliters of red paint. So: 5 units = 350 ml Step 2: Find the size of 1 unit. Divide both sides by 5: 1 unit = 350 / 5 1 unit = 70 ml Step 3: Find the amount of blue paint. Blue paint = 7 units = 7 × 70 ml Blue paint = 490 ml Step 4: Conclusion. To maintain the 5:7 ratio with 350 ml of red paint, Liam needs 490 ml of blue paint. Final answer: 490

6. Emma is baking cookies. A recipe requires 7 cups of flour for every 3 cups of sugar. If Emma uses 21 cups of flour, how many cups of sugar does she need? Answer: 9 Solution: Write the ratio of flour to sugar from the recipe: 7 cups flour / 3 cups sugar. Let x be the unknown cups of sugar. Set up the proportion: 7/3 = 21/x.
   Full step-by-step solution

   Step 1: Write the ratio of flour to sugar from the recipe: 7 cups flour / 3 cups sugar. Step 2: Let x be the unknown cups of sugar. Set up the proportion: 7/3 = 21/x. Step 3: Cross-multiply: 7 * x = 3 * 21. Step 4: Simplify: 7x = 63. Step 5: Divide both sides by 7: x = 63 / 7 = 9. The answer is 9 cups of sugar.

7. A wildlife conservation team is tracking the population growth of an endangered species. They observe that the current population of 1,200 animals is increasing at a rate where the ratio of new births to the existing population is 3:100 each year. If this growth rate continues, how many new animals will be born in the next year? Answer: 36 Solution: Identify the ratio of new births to existing population: 3:100 This means for every 100 animals in the population, 3 new animals are born each year.
   Full step-by-step solution

   Step 1: Identify the ratio of new births to existing population: 3:100 Step 2: This means for every 100 animals in the population, 3 new animals are born each year. Step 3: Set up a proportion to find the number of new births (x) for a population of 1,200 animals: 3/100 = x/1200 Step 4: Cross-multiply to solve for x: 100 * x = 3 * 1200 Step 5: Calculate: 100x = 3600 Step 6: Divide both sides by 100: x = 3600 ÷ 100 Step 7: x = 36 Therefore, 36 new animals will be born in the next year.

8. Emma is planning a community garden and needs to create a soil mixture using compost, topsoil, and sand in a 2:5:3 ratio. If she wants to make 1500 kilograms of soil mixture for the vegetable beds, how many kilograms of topsoil should she use? Answer: 750 Solution: Step 1: Add all the ratio parts together: 2 + 5 + 3 = 10 total parts Step 2: Determine what fraction of the mixture is topsoil: 5 parts out of 10 total parts = 5/10 = 1/2 Step 3: Calculate the amount of topsoil needed: 1/2 × 1500 kg = 750 kg Step 4: Verify the answer makes sense: 750 kg is…
   Full step-by-step solution

   Step 1: Add all the ratio parts together: 2 + 5 + 3 = 10 total parts Step 2: Determine what fraction of the mixture is topsoil: 5 parts out of 10 total parts = 5/10 = 1/2 Step 3: Calculate the amount of topsoil needed: 1/2 × 1500 kg = 750 kg Step 4: Verify the answer makes sense: 750 kg is exactly half of 1500 kg, which matches the fraction 1/2 The answer is 750 kilograms of topsoil.