Ratio Worksheets - Free Printable

The image you've uploaded is a Ratio Word Problems – Solve for x worksheet (Math Worksheet 17) with an answer key provided. It contains five ratio-based word problems, each with a step-by-step solution and final answer.

Let me walk through each problem, explain the reasoning, and verify the solutions.

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Problem 1:

> The ratio of girls to boys in a swimming club is 2:3. There are 18 girls. How many boys are there in the club?

Given:
- Ratio: girls : boys = 2:3
- Number of girls = 18

Solution:

We set up a proportion:
$$
\frac{\text{girls}}{\text{boys}} = \frac{2}{3} = \frac{18}{x}
$$

Cross-multiply:
$$
2x = 3 \times 18 = 54 \\
x = \frac{54}{2} = 27
$$

✔ Answer: 27 boys

✔️ Correct.

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Problem 2:

> Bea has dimes and quarters in the ratio of 1:4. If 22 of her coins are dimes, how many quarters does she have?

Given:
- Ratio: dimes : quarters = 1:4
- Dimes = 22

Solution:

Set up proportion:
$$
\frac{\text{dimes}}{\text{quarters}} = \frac{1}{4} = \frac{22}{x}
$$

Cross-multiply:
$$
1 \cdot x = 4 \cdot 22 = 88 \\
x = 88
$$

✔ Answer: 88 quarters

✔️ Correct.

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Problem 3:

> A fruit basket contains mangoes and cherries in the ratio of 3:10. If there are 9 mangoes, how many cherries are there?

Given:
- Ratio: mangoes : cherries = 3:10
- Mangoes = 9

Solution:

$$
\frac{3}{10} = \frac{9}{x}
$$

Cross-multiply:
$$
3x = 10 \cdot 9 = 90 \\
x = \frac{90}{3} = 30
$$

✔ Answer: 30 cherries

✔️ Correct.

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Problem 4:

> The ratio of red to green marbles in a bowl is 2:5. If there are 32 red marbles, how many total marbles are there in the bowl?

Given:
- Ratio: red : green = 2:5
- Red marbles = 32

Solution:

$$
\frac{2}{5} = \frac{32}{x} \quad \text{(where } x = \text{green marbles)}
$$

Cross-multiply:
$$
2x = 5 \cdot 32 = 160 \\
x = \frac{160}{2} = 80 \quad \text{(green marbles)}
$$

Total marbles = red + green = 32 + 80 = 112

✔ Answer: 112 marbles

✔️ Correct.

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Problem 5:

> A group of athletes are divided into blue and pink teams in the ratio of 4:5. If the blue team has 12 athletes, how many total athletes are there in all?

Given:
- Ratio: blue : pink = 4:5
- Blue team = 12

Solution:

$$
\frac{4}{5} = \frac{12}{x} \quad \text{(where } x = \text{pink team size)}
$$

Cross-multiply:
$$
4x = 5 \cdot 12 = 60 \\
x = \frac{60}{4} = 15 \quad \text{(pink team)}
$$

Total athletes = blue + pink = 12 + 15 = 27

✔ Answer: 27 athletes

✔️ Correct.

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✔ Summary of All Answers:

| Problem | Answer |
|--------|--------|
| 1 | 27 boys |
| 2 | 88 quarters |
| 3 | 30 cherries |
| 4 | 112 marbles |
| 5 | 27 athletes |

All solutions on the worksheet are correct and well-explained using proportions and cross-multiplication.

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🔍 General Strategy for Solving Ratio Word Problems:

1. Identify the ratio given (e.g., 2:3).
2. Assign variables to unknown quantities.
3. Set up a proportion using the ratio and known values.
4. Cross-multiply and solve for the unknown.
5. Check if the question asks for total (add parts if needed).

This method works consistently across all these types of problems.

Let me know if you'd like a printable version or want practice problems!