Ratio and Proportion Word Problems worksheet with six math problems and a red apple illustration.

Let's solve each of these ratio and proportion word problems step by step, showing all the work.

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Problem 1:

2 kilograms of apples cost $2.50. How many grams of apples can you buy for $20?

#### Step 1: Find the cost per kilogram
- 2 kg → $2.50
- So, 1 kg → $2.50 ÷ 2 = $1.25 per kg

#### Step 2: How many kilograms can you buy for $20?
- $20 ÷ $1.25 = 16 kilograms

#### Step 3: Convert kilograms to grams
- 1 kg = 1000 grams
- 16 kg = 16 × 1000 = 16,000 grams

✔ Answer: 16,000 grams

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Problem 2:

A truck can drive 200 kilometers on 25 liters of gasoline. How many liters of gasoline do I need to drive 640 kilometers?

Set up a proportion:

$$
\frac{200 \text{ km}}{25 \text{ L}} = \frac{640 \text{ km}}{x \text{ L}}
$$

Cross-multiply:

$$
200x = 25 \times 640 \\
200x = 16,000 \\
x = \frac{16,000}{200} = 80
$$

✔ Answer: 80 liters

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Problem 3:

A car can travel 120 miles in 90 minutes. How many hours will it take to drive 160 miles?

First, find the speed (miles per minute):

- 120 miles / 90 minutes = 1.333... miles per minute
Or better: simplify the ratio.

We can set up a proportion:

$$
\frac{120 \text{ miles}}{90 \text{ min}} = \frac{160 \text{ miles}}{x \text{ min}}
$$

Cross-multiply:

$$
120x = 90 \times 160 \\
120x = 14,400 \\
x = \frac{14,400}{120} = 120 \text{ minutes}
$$

Now convert minutes to hours:

- 120 minutes = 120 ÷ 60 = 2 hours

✔ Answer: 2 hours

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Problem 4:

I can type 100 words per 120 seconds. How many words can I type in 7 minutes?

First, convert 7 minutes to seconds:

- 7 × 60 = 420 seconds

Now set up a proportion:

$$
\frac{100 \text{ words}}{120 \text{ sec}} = \frac{x \text{ words}}{420 \text{ sec}}
$$

Cross-multiply:

$$
120x = 100 \times 420 \\
120x = 42,000 \\
x = \frac{42,000}{120} = 350
$$

✔ Answer: 350 words

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Problem 5:

A chicken can lay 1 egg per 2 days. How many hours will it take to lay 5 eggs?

First, determine how long it takes to lay 5 eggs:

- 1 egg → 2 days
- 5 eggs → 5 × 2 = 10 days

Now convert days to hours:

- 1 day = 24 hours
- 10 days = 10 × 24 = 240 hours

✔ Answer: 240 hours

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Problem 6:

I can run 6 kilometers per hour at a steady pace. How long will it take me to run 10 kilometers?

Use the formula:

$$
\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{10 \text{ km}}{6 \text{ km/h}} = \frac{10}{6} = \frac{5}{3} \text{ hours}
$$

Convert to minutes or mixed number:

- $ \frac{5}{3} = 1 \frac{2}{3} $ hours
- $ \frac{2}{3} $ of an hour = $ \frac{2}{3} \times 60 = 40 $ minutes

So, $ 1 \frac{2}{3} $ hours = 1 hour 40 minutes

✔ Answer: 1 hour 40 minutes (or $ \frac{5}{3} $ hours)

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✔ Final Answers:

1. 16,000 grams
2. 80 liters
3. 2 hours
4. 350 words
5. 240 hours
6. 1 hour 40 minutes

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