The local elementary school is having a contest to guess how many jellybeans are in a jar. The principal informs you that 80 jellybeans weigh 1.4 ounces, and that the weight of all the jellybeans in the jar is 112 ounces. Find the number of jellybeans in the jar by solving a proportion. Round to the nearest jellybean, if necessary.

To find the number of jellybeans in the jar, we can set up a proportion based on the information given:

1. **Given Information:**
   - 80 jellybeans weigh 1.4 ounces.
   - The total weight of jellybeans in the jar is 112 ounces.

2. **Setting Up the Proportion:**

   Let \( x \) represent the number of jellybeans in the jar. The proportion can be set up as follows:

   \[
   \frac{80 \text{ jellybeans}}{1.4 \text{ ounces}} = \frac{x \text{ jellybeans}}{112 \text{ ounces}}
   \]

3. **Solving the Proportion:**

   Cross-multiply to solve for \( x \):

   \[
   80 \times 112 = 1.4 \times x
   \]

   \[
   8960 = 1.4x
   \]

   Now, divide both sides by 1.4:

   \[
   x = \frac{8960}{1.4} = 6400
   \]

4. **Conclusion:**

   Therefore, there are approximately **6400 jellybeans** in the jar.

Would you like more details or have any questions?

Here are 5 related questions:
1. How would the number of jellybeans change if the weight of the jar was 56 ounces?
2. What is the weight of one jellybean based on the given information?
3. How would the proportion change if 100 jellybeans weighed 1.4 ounces?
4. How many jellybeans would be in the jar if it weighed 150 ounces?
5. What if the jellybeans weighed 2 ounces each; how many jellybeans would that be?

**Tip:** Always cross-multiply and then solve for the unknown when dealing with proportions.

Learn how to use proportions to solve for the number of jellybeans in a jar based on their weight. This problem teaches key concepts in proportions and cross-multiplication, suitable for students in Grades 6-8.

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