Ratio Concepts

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Ratio Concepts · Grade 6 · Worksheet 2

1. If the ratio of boys to girls in a school is 5:4 and there are 720 students total, how many boys are there? Answer: 400 Solution: The ratio of boys to girls is 5:4. This means for every 5 boys, there are 4 girls. Add the ratio parts together to find the total parts: 5 + 4 = 9 parts.
   Full step-by-step solution

   Step 1: The ratio of boys to girls is 5:4. This means for every 5 boys, there are 4 girls. Step 2: Add the ratio parts together to find the total parts: 5 + 4 = 9 parts. Step 3: The total number of students is 720. This represents 9 parts. Step 4: Find the value of one part by dividing the total students by the total parts: 720 ÷ 9 = 80 students per part. Step 5: Find the number of boys, who represent 5 parts: 5 × 80 = 400 boys. The answer is 400.

2. A school is organizing a field trip to a science museum. The total cost for the trip is $1,275, which needs to be divided equally among the 34 students attending. What is the cost per student? Answer: 37.5 Solution: Identify the total cost: $1,275 Identify the number of students: 34 Divide the total cost by the number of students: 1275 ÷ 34 Calculate 34 × 37 = 1258 Subtract: 1275 - 1258 = 17 Add decimal and continue: 17.0 ÷ 34 = 0.5 Combine results: 37 + 0.5 = 37.5 The cost per student is $37.50, which can…
   Full step-by-step solution

   Step 1: Identify the total cost: $1,275 Step 2: Identify the number of students: 34 Step 3: Divide the total cost by the number of students: 1275 ÷ 34 Step 4: Calculate 34 × 37 = 1258 Step 5: Subtract: 1275 - 1258 = 17 Step 6: Add decimal and continue: 17.0 ÷ 34 = 0.5 Step 7: Combine results: 37 + 0.5 = 37.5 Step 8: The cost per student is $37.50, which can be written as 37.5

3. If 5:7 = x:42, then x = ? Answer: 30 Solution: Write the proportion as an equation: 5/7 = x/42 Cross-multiply to eliminate the fractions: 5 × 42 = 7 × x Calculate 5 × 42 = 210 The equation becomes 210 = 7x Divide both sides by 7 to solve for x: 210 ÷ 7 = 30 Therefore, x = 30
   Full step-by-step solution

   Step 1: Write the proportion as an equation: 5/7 = x/42 Step 2: Cross-multiply to eliminate the fractions: 5 × 42 = 7 × x Step 3: Calculate 5 × 42 = 210 Step 4: The equation becomes 210 = 7x Step 5: Divide both sides by 7 to solve for x: 210 ÷ 7 = 30 Step 6: Therefore, x = 30

4. Charlotte is making fruit punch. The recipe calls for 7 cups of orange juice for every 2 cups of pineapple juice. If Charlotte uses 42 cups of orange juice, how many cups of pineapple juice does she need? Answer: 12 Solution: The ratio of orange juice to pineapple juice is 7:2. This means for every 7 cups of orange juice, we need 2 cups of pineapple juice. Charlotte uses 42 cups of orange juice.
   Full step-by-step solution

   Step 1: The ratio of orange juice to pineapple juice is 7:2. This means for every 7 cups of orange juice, we need 2 cups of pineapple juice. Step 2: Charlotte uses 42 cups of orange juice. Divide 42 by 7 to find how many groups of 7 there are: 42 ÷ 7 = 6 groups. Step 3: For each group of 7 cups of orange juice, we need 2 cups of pineapple juice. Multiply the number of groups by 2: 6 × 2 = 12. Step 4: Charlotte needs 12 cups of pineapple juice. The answer is 12.

5. Aroha is baking cookies. The recipe uses a ratio of 12 cups of flour to 5 cups of sugar. If Aroha uses 36 cups of flour, how many cups of sugar does she need? Answer: 15 Solution: The original ratio of flour to sugar is 12:5. Step 2: Aroha uses 36 cups of flour. Find the multiplier: 36 ÷ 12 = 3.
   Full step-by-step solution

   Step 1: The original ratio of flour to sugar is 12:5. Step 2: Aroha uses 36 cups of flour. Find the multiplier: 36 ÷ 12 = 3. Step 3: Multiply the original amount of sugar by the same multiplier: 5 × 3 = 15. Step 4: Aroha needs 15 cups of sugar. The answer is 15.

6. If the ratio of students to teachers on a field trip is 15:2 and there are 210 students, how many teachers are there? Answer: 28 Solution: Write the ratio as a fraction: students/teachers = 15/2 Set up the proportion with the known number of students: 15/2 = 210/x Cross-multiply: 15 × x = 2 × 210 Calculate: 15x = 420 Divide both sides by 15: x = 420 ÷ 15 Calculate: x = 28 There are 28 teachers on the field trip.
   Full step-by-step solution

   Step 1: Write the ratio as a fraction: students/teachers = 15/2 Step 2: Set up the proportion with the known number of students: 15/2 = 210/x Step 3: Cross-multiply: 15 × x = 2 × 210 Step 4: Calculate: 15x = 420 Step 5: Divide both sides by 15: x = 420 ÷ 15 Step 6: Calculate: x = 28 There are 28 teachers on the field trip.

7. 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 3:5 ratio. If Liam uses 450 milliliters of red paint, how many milliliters of blue paint should he use to maintain the correct ratio? Answer: 750 Solution: We are told that the ratio of red paint to blue paint is 3:5. This means for every 3 parts of red paint, we need 5 parts of blue paint. Write the ratio as a fraction.
   Full step-by-step solution

   We are told that the ratio of red paint to blue paint is 3:5. This means for every 3 parts of red paint, we need 5 parts of blue paint. Step 1: Write the ratio as a fraction. Red / Blue = 3 / 5. Step 2: We know the amount of red paint used is 450 milliliters. Let the amount of blue paint be B milliliters. Step 3: Set up the proportion: 450 / B = 3 / 5. Step 4: Cross-multiply to solve for B: 450 * 5 = 3 * B. Step 5: Calculate: 2250 = 3 * B. Step 6: Divide both sides by 3: B = 2250 / 3. Step 7: Perform the division: B = 750. So, Liam should use 750 milliliters of blue paint.

8. Matiu is making a fruit punch. The recipe calls for 4 parts orange juice to 7 parts lemonade. If Matiu uses 36 cups of orange juice, how many cups of lemonade does he need? Answer: 63 Solution: The ratio of orange juice to lemonade is 4:7. This means for every 4 cups of orange juice, you need 7 cups of lemonade. Matiu uses 36 cups of orange juice.
   Full step-by-step solution

   Step 1: The ratio of orange juice to lemonade is 4:7. This means for every 4 cups of orange juice, you need 7 cups of lemonade. Step 2: Matiu uses 36 cups of orange juice. Find how many groups of 4 are in 36: 36 ÷ 4 = 9 groups. Step 3: For each group, you need 7 cups of lemonade. So multiply: 9 × 7 = 63 cups of lemonade. Step 4: Check: The ratio 36:63 simplifies to 4:7 (divide both by 9). The answer is 63.

9. Ava is making a fruit salad. The ratio of strawberries to blueberries is 6:1. If she uses 36 strawberries, how many blueberries does she need? Answer: 6 Solution: The ratio of strawberries to blueberries is 6:1, meaning for every 6 strawberries, there is 1 blueberry. Ava uses 36 strawberries. Divide 36 by 6 to find how many groups of 6 strawberries there are: 36 ÷ 6 = 6 groups.
   Full step-by-step solution

   Step 1: The ratio of strawberries to blueberries is 6:1, meaning for every 6 strawberries, there is 1 blueberry. Step 2: Ava uses 36 strawberries. Divide 36 by 6 to find how many groups of 6 strawberries there are: 36 ÷ 6 = 6 groups. Step 3: Since each group has 1 blueberry, multiply the number of groups by 1: 6 × 1 = 6 blueberries. Step 4: Therefore, Ava needs 6 blueberries. The answer is 6.