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Equivalent Ratio Tables

Grade 6 · Ratios · Worksheet 2

  1. If 7:9 = x:63, then x = ? Answer: ______________
  2. Mason is making lemonade. The recipe calls for 7 cups of water for every 2 cups of lemon juice. Complete the table of equivalent ratios to find how many cups of water are needed for 12 cups of lemon juice. | Lemon Juice (cups) | Water (cups) | |-------------------|-------------| | 2 | 7 | | 4 | 14 | | 6 | 21 | | 8 | 28 | | 10 | 35 | | 12 | ? | Answer: ______________
  3. A wildlife sanctuary is tracking the population of deer and elk in their preserve. The current ratio of deer to elk is 7:4. If there are 1,540 deer in the sanctuary, how many elk are there? Answer: ______________
  4. If 3:8 = x:120, then x = ? Answer: ______________
  5. A recipe for lemonade requires mixing 5 cups of water with 2 cups of lemon juice. If Liam wants to make a large batch using 15 cups of water, how many cups of lemon juice should he use to maintain the same flavor? Answer: ______________
  6. A wildlife sanctuary is tracking the population of deer and elk in their preserve. The current ratio of deer to elk is 7:4. If there are 1,540 animals in total, how many elk are in the sanctuary? Answer: ______________
  7. Liam is mixing paint for his art project. He needs to create a specific shade of purple by mixing red and blue paint in a ratio of 3:5. If Liam uses 2.4 liters of blue paint, how many liters of red paint should he use to maintain the correct ratio? Answer: ______________
  8. A fruit punch recipe calls for mixing grape juice and orange juice in a ratio of 3:2. If Liam wants to make 15 cups of fruit punch, how many cups of grape juice does he need? Answer: ______________
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Answer Key & Explanations

Equivalent Ratio Tables · Grade 6 · Worksheet 2

  1. If 7:9 = x:63, then x = ? Answer: 49 Solution: Write the proportion as an equation: 7/9 = x/63 Cross-multiply to eliminate the fractions: 7 * 63 = 9 * x Calculate 7 * 63 = 441 The equation is now 441 = 9x Divide both sides by 9 to solve for x: x = 441 ÷ 9 Calculate 441 ÷ 9 = 49 Therefore, x = 49
    Full step-by-step solution

    Step 1: Write the proportion as an equation: 7/9 = x/63 Step 2: Cross-multiply to eliminate the fractions: 7 * 63 = 9 * x Step 3: Calculate 7 * 63 = 441 Step 4: The equation is now 441 = 9x Step 5: Divide both sides by 9 to solve for x: x = 441 ÷ 9 Step 6: Calculate 441 ÷ 9 = 49 Step 7: Therefore, x = 49

  2. Mason is making lemonade. The recipe calls for 7 cups of water for every 2 cups of lemon juice. Complete the table of equivalent ratios to find how many cups of water are needed for 12 cups of lemon juice. | Lemon Juice (cups) | Water (cups) | |-------------------|-------------| | 2 | 7 | | 4 | 14 | | 6 | 21 | | 8 | 28 | | 10 | 35 | | 12 | ? | Answer: 42 Solution: Identify the ratio from the first row: 2 cups lemon juice : 7 cups water. To find water for 12 cups lemon juice, set up a proportion: 2/7 = 12/x. Cross-multiply: 2 * x = 7 * 12.
    Full step-by-step solution

    Step 1: Identify the ratio from the first row: 2 cups lemon juice : 7 cups water. Step 2: To find water for 12 cups lemon juice, set up a proportion: 2/7 = 12/x. Step 3: Cross-multiply: 2 * x = 7 * 12. Step 4: Calculate the right side: 7 * 12 = 84. Step 5: Write the equation: 2x = 84. Step 6: Divide both sides by 2: x = 84 / 2 = 42. Step 7: So, 42 cups of water are needed for 12 cups of lemon juice. The answer is 42.

  3. A wildlife sanctuary is tracking the population of deer and elk in their preserve. The current ratio of deer to elk is 7:4. If there are 1,540 deer in the sanctuary, how many elk are there? Answer: 880 Solution: The ratio of deer to elk is 7:4, which means for every 7 deer, there are 4 elk. We know there are 1,540 deer, which represents 7 parts of the ratio.
    Full step-by-step solution

    Step 1: The ratio of deer to elk is 7:4, which means for every 7 deer, there are 4 elk. Step 2: We know there are 1,540 deer, which represents 7 parts of the ratio. Step 3: Find the value of one ratio part by dividing the number of deer by 7: 1,540 ÷ 7 = 220 Step 4: Since there are 4 parts for elk, multiply the value of one part by 4: 220 × 4 = 880 Step 5: Therefore, there are 880 elk in the sanctuary.

  4. If 3:8 = x:120, then x = ? Answer: 45 Solution: Write the proportion as fractions: 3/8 = x/120 Cross multiply: 3 × 120 = 8 × x Calculate left side: 360 = 8x Divide both sides by 8: 360 ÷ 8 = x Calculate: 45 = x The answer is 45.
    Full step-by-step solution

    Step 1: Write the proportion as fractions: 3/8 = x/120 Step 2: Cross multiply: 3 × 120 = 8 × x Step 3: Calculate left side: 360 = 8x Step 4: Divide both sides by 8: 360 ÷ 8 = x Step 5: Calculate: 45 = x The answer is 45.

  5. A recipe for lemonade requires mixing 5 cups of water with 2 cups of lemon juice. If Liam wants to make a large batch using 15 cups of water, how many cups of lemon juice should he use to maintain the same flavor? Answer: 6 Solution: The recipe says 5 cups of water to 2 cups of lemon juice. Identify the new amount of water. Liam is using 15 cups of water.
    Full step-by-step solution

    Step 1: Understand the original ratio. The recipe says 5 cups of water to 2 cups of lemon juice. So the ratio of water to lemon juice is 5 : 2. Step 2: Identify the new amount of water. Liam is using 15 cups of water. Step 3: Find the scaling factor. We see that 15 cups of water is 3 times the original 5 cups because: 15 ÷ 5 = 3. Step 4: Apply the scaling factor to the lemon juice. Original lemon juice = 2 cups. Multiply by the same scaling factor: 2 × 3 = 6 cups. Step 5: Conclusion. To keep the same flavor, Liam should use 6 cups of lemon juice. Final answer: 6

  6. A wildlife sanctuary is tracking the population of deer and elk in their preserve. The current ratio of deer to elk is 7:4. If there are 1,540 animals in total, how many elk are in the sanctuary? Answer: 560 Solution: The ratio of deer to elk is 7:4. This means for every 7 + 4 = 11 animals, 7 are deer and 4 are elk. The total number of animals is 1,540.
    Full step-by-step solution

    Step 1: The ratio of deer to elk is 7:4. This means for every 7 + 4 = 11 animals, 7 are deer and 4 are elk. Step 2: The total number of animals is 1,540. Step 3: Find the value of one 'ratio part' by dividing the total by the sum of the ratio parts: 1,540 / 11 = 140. Step 4: Multiply the value of one part by the number of parts for elk: 140 * 4 = 560. The answer is 560 elk.

  7. Liam is mixing paint for his art project. He needs to create a specific shade of purple by mixing red and blue paint in a ratio of 3:5. If Liam uses 2.4 liters of blue paint, how many liters of red paint should he use to maintain the correct ratio? Answer: 1.44 Solution: We are told the ratio of red to blue paint is 3:5. That means for every 3 parts red, there are 5 parts blue. Write the ratio as a fraction.
    Full step-by-step solution

    We are told the ratio of red to blue paint is 3:5. That means for every 3 parts red, there are 5 parts blue. Step 1: Write the ratio as a fraction. Red / Blue = 3 / 5 Step 2: We know the amount of blue paint is 2.4 liters. Let R be the liters of red paint needed. So: R / 2.4 = 3 / 5 Step 3: Solve for R. Multiply both sides by 2.4: R = (3 / 5) × 2.4 Step 4: Calculate. First, 3 / 5 = 0.6 Then, 0.6 × 2.4 = 1.44 Step 5: Conclusion. Liam should use 1.44 liters of red paint. Final answer: 1.44

  8. A fruit punch recipe calls for mixing grape juice and orange juice in a ratio of 3:2. If Liam wants to make 15 cups of fruit punch, how many cups of grape juice does he need? Answer: 9 Solution: The ratio of grape juice to orange juice is 3:2. This means for every 3 parts grape juice, there are 2 parts orange juice. Liam wants 15 cups total.
    Full step-by-step solution

    Let's solve this step-by-step. Step 1: Understand the ratio The ratio of grape juice to orange juice is 3:2. This means for every 3 parts grape juice, there are 2 parts orange juice. So the total parts in the mixture = 3 + 2 = 5 parts. Step 2: Relate parts to total quantity Liam wants 15 cups total. So 5 parts = 15 cups. Therefore, 1 part = 15 cups ÷ 5 = 3 cups. Step 3: Find grape juice quantity Grape juice is 3 parts. So grape juice = 3 parts × 3 cups per part = 9 cups. Step 4: Conclusion Liam needs 9 cups of grape juice. Final answer: 9