Each worker can paint 2 large houses or 3 small houses in 3 hours. The contractor wants to have 20 large houses and 700 small houses painted in 3 hours. How many workers are needed




Let's break this problem down step by step.

### Step 1: Calculate how many houses one worker can paint.
A single worker can either paint:
- 2 large houses in 3 hours, or
- 3 small houses in 3 hours.

### Step 2: Define the total work.
The contractor needs:
- 20 large houses painted.
- 700 small houses painted.

### Step 3: Convert the work into a common measure (like "worker-hours").

For large houses:
- Each worker can paint 2 large houses in 3 hours.
- To paint 20 large houses, you would need \( \frac{20}{2} = 10 \) workers.

For small houses:
- Each worker can paint 3 small houses in 3 hours.
- To paint 700 small houses, you would need \( \frac{700}{3} \approx 233.33 \) workers.

### Step 4: Combine the number of workers needed.
- For large houses: 10 workers
- For small houses: 234 workers (rounding up from 233.33)

### Step 5: Total number of workers.
Total number of workers needed is:
\[ 10 + 234 = 244 \]

So, **244 workers** are needed to complete the job in 3 hours.

Would you like more details or have any questions about the process?

Here are 5 related questions:
1. What if each worker could paint 4 small houses in 3 hours instead?
2. How many workers would be needed if the contractor only wanted to paint 500 small houses?
3. What if the workers had 6 hours instead of 3 hours to finish the job?
4. How would the number of workers change if they could only paint 1 large house in 3 hours?
5. How many workers would be needed if 50 large houses needed painting instead?

**Tip:** Always convert tasks into units that make comparison easy, like "worker-hours" or "work per unit time."

Each worker can paint 2 large houses or 3 small houses in 3 hours. The contractor wants to have 20 large houses and 700 small houses painted in 3 hours. How many workers are needed?

Learn how to calculate the number of workers needed to paint 20 large houses and 700 small houses in 3 hours. This problem involves key concepts in ratios, proportions, and work-rate calculations. Suitable for students in Grades 6-8.

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