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Finding the Third Proportional to 646 and 709

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Solution

The third proportional to 646 and 709 is: 778.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    646 : 709 = 709 : x
  2. Step 2: Convert to fraction form
    646/709 = 709/x
  3. Step 3: Cross multiply
    646x = 709 × 709
  4. Step 4: Simplify right side
    646x = 502,681
  5. Step 5: Solve for x
    x = 502,681/646
  6. Step 6: Final answer
    x = 778.14

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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.