Ratio and Proportions Word Problems Worksheets - Free Printable

Here's the step-by-step solution to all 10 Grade 7 Ratio Word Problems:

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1. Recipe Scaling:
> A cookie recipe makes 24 cookies using 2 cups of flour. How much flour is needed to make 36 cookies?

- Set up a proportion:
\[
\frac{2 \text{ cups}}{24 \text{ cookies}} = \frac{x \text{ cups}}{36 \text{ cookies}}
\]
- Cross-multiply:
\[
24x = 2 \times 36 = 72
\]
- Solve for \( x \):
\[
x = \frac{72}{24} = 3
\]

✔ Answer: 3 cups of flour

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2. Painting Time:
> It takes 4 hours for 6 painters to complete a mural. How many hours will it take for 10 painters to complete the same mural?

- This is an inverse proportion — more painters = less time.
- Total “painter-hours” = 6 painters × 4 hours = 24 painter-hours.
- For 10 painters:
\[
\text{Time} = \frac{24}{10} = 2.4 \text{ hours}
\]
(or 2 hours and 24 minutes)

✔ Answer: 2.4 hours

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3. Proportional Relationships:
> The ratio of the number of miles driven to the number of gallons of gas used is 30:2. How many gallons of gas would be used to drive 90 miles?

- Simplify the ratio: 30 miles : 2 gallons → 15 miles per gallon.
- So, for 90 miles:
\[
\frac{90}{15} = 6 \text{ gallons}
\]
Or set up proportion:
\[
\frac{30}{2} = \frac{90}{x} \Rightarrow 30x = 180 \Rightarrow x = 6
\]

✔ Answer: 6 gallons

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4. Fruit Smoothies:
> A smoothie recipe calls for a ratio of 2 cups of strawberries to 3 cups of yogurt. If you want to make 6 cups of smoothie, how many cups of yogurt should you use?

- Total parts in ratio: 2 (strawberries) + 3 (yogurt) = 5 parts.
- Yogurt is 3 out of 5 parts.
- So for 6 cups total:
\[
\frac{3}{5} \times 6 = \frac{18}{5} = 3.6 \text{ cups}
\]

✔ Answer: 3.6 cups of yogurt

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5. Train Speed:
> A train travels 200 miles in 4 hours. At the same speed, how far can it travel in 10 hours?

- Speed = distance/time = 200 ÷ 4 = 50 mph.
- In 10 hours: 50 × 10 = 500 miles.

✔ Answer: 500 miles

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6. Candy Mix:
> A bag of candies contains a ratio of 3 red candies to 5 blue candies. If there are 18 red candies, how many blue candies are there?

- Set up proportion:
\[
\frac{3}{5} = \frac{18}{x}
\]
- Cross-multiply:
\[
3x = 90 \Rightarrow x = 30
\]

✔ Answer: 30 blue candies

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7. Dance Party:
> In a dance party, the ratio of boys to girls is 2:3. If there are 24 boys, how many girls are there?

- Set up proportion:
\[
\frac{2}{3} = \frac{24}{x}
\]
- Cross-multiply:
\[
2x = 72 \Rightarrow x = 36
\]

✔ Answer: 36 girls

---

8. Coin Collection:
> In a coin collection, the ratio of quarters to dimes is 5:2. If there are 15 dimes, how many quarters are there?

- Set up proportion:
\[
\frac{5}{2} = \frac{x}{15}
\]
- Cross-multiply:
\[
2x = 75 \Rightarrow x = 37.5
\]
❗ Wait — this gives 37.5 quarters? That’s not possible with real coins.

Let’s recheck: Maybe we misread.

Actually, if ratio is 5 quarters : 2 dimes, and there are 15 dimes:

- Number of “groups” of 2 dimes = 15 ÷ 2 = 7.5
- Then quarters = 5 × 7.5 = 37.5

But since you can’t have half a quarter, perhaps the problem expects the proportional answer even if unrealistic.

✔ Answer: 37.5 quarters *(Note: In real life, this wouldn't happen — likely a math exercise)*

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9. Coffee Mixing:
> A coffee blend consists of a ratio of 1 part dark roast to 4 parts medium roast. If you have 8 ounces of dark roast, how many ounces of medium roast should you use?

- Ratio: 1 : 4 → for every 1 oz dark roast, use 4 oz medium roast.
- So for 8 oz dark roast: 8 × 4 = 32 oz medium roast.

✔ Answer: 32 ounces of medium roast

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10. Marathon Training:
> A runner can run 5 miles in 40 minutes. At the same speed, how long would it take to run 13.1 miles?

- First, find speed: 5 miles / 40 min = 0.125 miles per minute.
- Time for 13.1 miles: 13.1 ÷ 0.125 = 104.8 minutes.
- OR set up proportion:
\[
\frac{5}{40} = \frac{13.1}{x} \Rightarrow 5x = 524 \Rightarrow x = 104.8
\]

✔ Answer: 104.8 minutes (or 1 hour 44 minutes 48 seconds)

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## ✔ Final Answers Summary:

1. 3 cups
2. 2.4 hours
3. 6 gallons
4. 3.6 cups
5. 500 miles
6. 30 blue candies
7. 36 girls
8. 37.5 quarters
9. 32 ounces
10. 104.8 minutes

Let me know if you’d like any explanation expanded or visualized!