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Finding the Third Proportional to 7,705 and 14,423

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Solution

The third proportional to 7,705 and 14,423 is: 26,998.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,705 : 14,423 = 14,423 : x
  2. Step 2: Convert to fraction form
    7,705/14,423 = 14,423/x
  3. Step 3: Cross multiply
    7,705x = 14,423 × 14,423
  4. Step 4: Simplify right side
    7,705x = 208,022,929
  5. Step 5: Solve for x
    x = 208,022,929/7,705
  6. Step 6: Final answer
    x = 26,998.43

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Why These Related Problems?

These problems maintain the same ratio (1.87) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.