Ratios Word Problems - Teach-nology - Free Printable

Let's solve each of the ratio word problems step by step.

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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?

Given:
- Ratio of boys : girls = 7 : 11
- Number of boys = 49

We can set up a proportion based on the ratio:

$$
\frac{7}{11} = \frac{49}{x}
$$

Where $ x $ is the number of girls.

Cross-multiply:

$$
7x = 11 \times 49 = 539
$$

$$
x = \frac{539}{7} = 77
$$

So, there are 77 girls.

Total students = boys + girls = $ 49 + 77 = 126 $

✔ Answer: 126 students altogether

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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?

Given:
- Ratio of marbles : stones = 6 : 7
- Marbles = 42

Set up proportion:

$$
\frac{6}{7} = \frac{42}{x}
$$

Cross-multiply:

$$
6x = 7 \times 42 = 294
$$

$$
x = \frac{294}{6} = 49
$$

✔ Answer: 49 stones

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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?

Given:
- Coins : Notes = 3 : 8
- Coins = 24

Set up proportion:

$$
\frac{3}{8} = \frac{24}{x}
$$

Cross-multiply:

$$
3x = 8 \times 24 = 192
$$

$$
x = \frac{192}{3} = 64
$$

✔ Answer: 64 notes

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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?

Given:
- Black : Blue = 5 : 3
- Black bags = 10

Set up proportion:

$$
\frac{5}{3} = \frac{10}{x}
$$

Cross-multiply:

$$
5x = 3 \times 10 = 30
$$

$$
x = \frac{30}{5} = 6
$$

✔ Answer: 6 blue bags

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

Given:
- Trucks : Cars = 7 : 8
- Trucks = 21

Set up proportion:

$$
\frac{7}{8} = \frac{21}{x}
$$

Cross-multiply:

$$
7x = 8 \times 21 = 168
$$

$$
x = \frac{168}{7} = 24
$$

✔ Answer: 24 cars

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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?

Given:
- Red : Green = 4 : 6 (which simplifies to 2:3, but we'll use 4:6)
- Red ribbons = 32

Set up proportion:

$$
\frac{4}{6} = \frac{32}{x}
$$

Cross-multiply:

$$
4x = 6 \times 32 = 192
$$

$$
x = \frac{192}{4} = 48
$$

✔ Answer: 48 green ribbons

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

Given:
- Ratio of Container 1 : Container 2 = 6 : 7
- Volume of first container = 36 liters

Set up proportion:

$$
\frac{6}{7} = \frac{36}{x}
$$

Cross-multiply:

$$
6x = 7 \times 36 = 252
$$

$$
x = \frac{252}{6} = 42
$$

✔ 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

Let me know if you'd like these explained visually or with diagrams!