Ratio and Proportions Word Problems Worksheets - Free Printable

Let's solve each of these Grade 7 Ratio Word Problems step by step. I'll explain the reasoning and calculations for each.

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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?

Step-by-step:

- The ratio of cookies to flour is:
$ \frac{24 \text{ cookies}}{2 \text{ cups}} = 12 \text{ cookies per cup} $

- So, 1 cup of flour → 12 cookies

- To make 36 cookies:
$ \frac{36}{12} = 3 $ cups of flour

✔ 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?

Assumption: All painters work at the same rate.

- Total work = 6 painters × 4 hours = 24 painter-hours

- Now, if 10 painters are working, time required:
$ \frac{24 \text{ painter-hours}}{10 \text{ painters}} = 2.4 $ hours

- Convert 0.4 hours to minutes: $ 0.4 × 60 = 24 $ minutes

✔ Answer: 2.4 hours or 2 hours and 24 minutes

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3. Proportional Relationship:

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

- Simplify the ratio:
$ \frac{30}{2} = 15 $ miles per gallon

- So, for 90 miles:
$ \frac{90}{15} = 6 $ gallons

✔ 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 the mixture: 2 (strawberries) + 3 (yogurt) = 5 parts

- Each part = $ \frac{6}{5} = 1.2 $ cups

- Yogurt = 3 parts → $ 3 × 1.2 = 3.6 $ 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 = $ \frac{200}{4} = 50 $ miles per hour

- 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?

- Ratio: Red : Blue = 3 : 5

- 3 parts = 18 red candies → 1 part = $ \frac{18}{3} = 6 $

- Blue candies = 5 parts → $ 5 × 6 = 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?

- Ratio: Boys : Girls = 2 : 3

- 2 parts = 24 boys → 1 part = $ \frac{24}{2} = 12 $

- Girls = 3 parts → $ 3 × 12 = 36 $

✔ Answer: 36 girls

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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?

- Ratio: Quarters : Dimes = 5 : 2

- 2 parts = 15 dimes → 1 part = $ \frac{15}{2} = 7.5 $

- Quarters = 5 parts → $ 5 × 7.5 = 37.5 $

Wait! That’s not possible — we can’t have half a coin.

But let’s double-check:

- 2 parts = 15 dimes → so each "part" is $ 15 ÷ 2 = 7.5 $

- Then 5 parts = $ 5 × 7.5 = 37.5 $ → still not valid

But ratios must scale evenly. Let’s try solving with proportion:

$ \frac{5}{2} = \frac{x}{15} $

Cross-multiply:
$ 2x = 75 $ → $ x = 37.5 $

This suggests a problem — unless fractional coins are allowed, this scenario isn't realistic.

But since it's a math problem, perhaps we accept the mathematical answer.

However, maybe there's a typo? Or perhaps the number of dimes is meant to be divisible by 2.

But assuming the problem is correct as given:

✔ Answer: 37.5 quarters → But since you can't have half a quarter, this implies an inconsistency, or the problem expects a decimal answer.

Alternatively, check if 15 dimes fits the ratio.

If ratio is 5:2, then total coins must be in multiples of 7 (5+2), but here only dimes are given.

So, if dimes = 2 parts = 15 → parts = 7.5 → quarters = 5 × 7.5 = 37.5

So, mathematically, the answer is 37.5, but in real life, it's impossible.

✔ Answer: 37.5 quarters (though unusual)

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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: Dark : Medium = 1 : 4

- 1 part = 8 oz → 4 parts = $ 4 × 8 = 32 $ oz

✔ 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?

- Speed = $ \frac{5 \text{ miles}}{40 \text{ min}} = 0.125 $ miles per minute

- Time for 13.1 miles:
$ \frac{13.1}{0.125} = 104.8 $ minutes

- Convert 0.8 minutes to seconds: $ 0.8 × 60 = 48 $ seconds

✔ Answer: 104 minutes and 48 seconds

Or, simplify via proportion:

$ \frac{5}{40} = \frac{13.1}{x} $

Cross-multiply:
$ 5x = 40 × 13.1 = 524 $
$ x = \frac{524}{5} = 104.8 $ minutes → same result

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1 | 3 cups of flour |
| 2 | 2.4 hours (or 2h 24m) |
| 3 | 6 gallons |
| 4 | 3.6 cups of yogurt |
| 5 | 500 miles |
| 6 | 30 blue candies |
| 7 | 36 girls |
| 8 | 37.5 quarters *(note: unusual, possibly error in problem setup)* |
| 9 | 32 ounces of medium roast |
| 10 | 104.8 minutes (104 min 48 sec) |

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Let me know if you'd like these explained in a printable format or need visual models (like tape diagrams) for any of them!