Ratio Word Problems Worksheets - Free Printable

Sure! Let’s solve each of the 7 ratio word problems step by step, explaining the reasoning behind each solution.

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Problem 1:
> The ratio of boys to girls in a classroom is 7 to 11. If there are a total of 49 boys in the classroom, then how many boys and girls are there altogether?

Solution:

- Ratio: Boys : Girls = 7 : 11
- We’re told there are 49 boys.
- Since 7 parts = 49 boys, we find the value of 1 part:

> 49 ÷ 7 = 7

- So, each “part” represents 7 students.
- Girls = 11 parts × 7 = 77 girls
- Total students = boys + girls = 49 + 77 = 126

✔ Answer: 126 students altogether

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Problem 2:
> The ratio of marbles to stones in a large pot is 6 to 7. If there are 42 marbles, then how many stones are there?

Solution:

- Ratio: Marbles : Stones = 6 : 7
- 6 parts = 42 marbles → 1 part = 42 ÷ 6 = 7
- Stones = 7 parts × 7 = 49 stones

✔ Answer: 49 stones

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Problem 3:
> The ratio of coins to notes in a bag is 3 to 8. If there are a total of 24 coins, then how many notes are there?

Solution:

- Ratio: Coins : Notes = 3 : 8
- 3 parts = 24 coins → 1 part = 24 ÷ 3 = 8
- Notes = 8 parts × 8 = 64 notes

✔ Answer: 64 notes

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Problem 4:
> The ratio of black bags to blue bags is 5 to 3. If there are a total of 10 black bags, then how many blue bags are there?

Solution:

- Ratio: Black : Blue = 5 : 3
- 5 parts = 10 black bags → 1 part = 10 ÷ 5 = 2
- Blue bags = 3 parts × 2 = 6 blue bags

✔ Answer: 6 blue bags

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Problem 5:
> The ratio of trucks to cars is 7 to 8. If there are a total of 21 trucks, how many cars are there?

Solution:

- Ratio: Trucks : Cars = 7 : 8
- 7 parts = 21 trucks → 1 part = 21 ÷ 7 = 3
- Cars = 8 parts × 3 = 24 cars

✔ Answer: 24 cars

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Problem 6:
> The ratio of red ribbons to green ribbons is 4 to 6. If there are a total of 32 red ribbons, then how many green ribbons are there?

Solution:

- Ratio: Red : Green = 4 : 6 (can simplify to 2:3, but not necessary)
- 4 parts = 32 red ribbons → 1 part = 32 ÷ 4 = 8
- Green ribbons = 6 parts × 8 = 48 green ribbons

✔ Answer: 48 green ribbons

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Problem 7:
> The volume of water in two containers is in the ratio of 6 to 7. If the volume of first container is 36 liters, find the volume of second container?

Solution:

- Ratio: Container 1 : Container 2 = 6 : 7
- 6 parts = 36 liters → 1 part = 36 ÷ 6 = 6 liters
- Container 2 = 7 parts × 6 = 42 liters

✔ Answer: 42 liters

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## ✔ Final Answers Summary:

1. 126 students
2. 49 stones
3. 64 notes
4. 6 blue bags
5. 24 cars
6. 48 green ribbons
7. 42 liters

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💡 Key Concept:

In all these problems, we use the idea of “parts” in a ratio. Once you know the value of one part (by dividing the known quantity by its corresponding ratio number), you can multiply that by the other part’s number to find the unknown quantity.

Let me know if you’d like a visual diagram or worksheet-style answer key!