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Finding the Third Proportional to 32,154 and 77,457

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Solution

The third proportional to 32,154 and 77,457 is: 186,589.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    32,154 : 77,457 = 77,457 : x
  2. Step 2: Convert to fraction form
    32,154/77,457 = 77,457/x
  3. Step 3: Cross multiply
    32,154x = 77,457 × 77,457
  4. Step 4: Simplify right side
    32,154x = 5,999,586,849
  5. Step 5: Solve for x
    x = 5,999,586,849/32,154
  6. Step 6: Final answer
    x = 186,589.13

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Why These Related Problems?

These problems maintain the same ratio (2.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.