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Finding the Third Proportional to 709 and 780

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Solution

The third proportional to 709 and 780 is: 858.11

Step by Step Solution

  1. Step 1: Write the proportion equation
    709 : 780 = 780 : x
  2. Step 2: Convert to fraction form
    709/780 = 780/x
  3. Step 3: Cross multiply
    709x = 780 × 780
  4. Step 4: Simplify right side
    709x = 608,400
  5. Step 5: Solve for x
    x = 608,400/709
  6. Step 6: Final answer
    x = 858.11

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.