i need to make the following cuts from boards that are 192" long: 90, 90, 85, 85. how many boards do i need?

You are trying to make the following cuts from boards that are each 192 inches long: 90, 90, 85, and 85 inches.

Let's check if we can minimize the number of boards used:

1. **First Board**:  
   - 90 inches cut  
   - Remaining: 192 - 90 = 102 inches
   - 85 inches cut  
   - Remaining: 102 - 85 = 17 inches (scrap)

2. **Second Board**:  
   - 90 inches cut  
   - Remaining: 192 - 90 = 102 inches
   - 85 inches cut  
   - Remaining: 102 - 85 = 17 inches (scrap)

Each board allows you to make one 90-inch cut and one 85-inch cut, leaving 17 inches as scrap. Therefore, to make all the cuts (90, 90, 85, 85), you will need **2 boards**.

Would you like further details or have any questions?

Here are 5 related questions to explore:

1. What happens if the boards are not exactly 192" long?
2. How would the answer change if you needed cuts of different lengths?
3. How could you reuse the scrap pieces efficiently in future projects?
4. What are other strategies for minimizing waste when cutting boards?
5. Could there be a way to optimize the cuts further with more advanced tools?

**Tip:** Always measure the cuts and boards precisely before starting to minimize waste.

Find out how many 192-inch boards are needed to make cuts of 90, 90, 85, and 85 inches. Learn about optimization techniques to minimize waste and understand key mathematical concepts related to subtraction and efficient resource usage. Suitable for students in Grades 6-8.

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