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Finding the Third Proportional to 10,970 and 16,457

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Solution

The third proportional to 10,970 and 16,457 is: 24,688.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,970 : 16,457 = 16,457 : x
  2. Step 2: Convert to fraction form
    10,970/16,457 = 16,457/x
  3. Step 3: Cross multiply
    10,970x = 16,457 × 16,457
  4. Step 4: Simplify right side
    10,970x = 270,832,849
  5. Step 5: Solve for x
    x = 270,832,849/10,970
  6. Step 6: Final answer
    x = 24,688.50

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.