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Finding the Third Proportional to 10,706 and 16,509

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Solution

The third proportional to 10,706 and 16,509 is: 25,457.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,706 : 16,509 = 16,509 : x
  2. Step 2: Convert to fraction form
    10,706/16,509 = 16,509/x
  3. Step 3: Cross multiply
    10,706x = 16,509 × 16,509
  4. Step 4: Simplify right side
    10,706x = 272,547,081
  5. Step 5: Solve for x
    x = 272,547,081/10,706
  6. Step 6: Final answer
    x = 25,457.41

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Why These Related Problems?

These problems maintain the same ratio (1.54) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.