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Finding the Third Proportional to 83,416 and 121,569

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Solution

The third proportional to 83,416 and 121,569 is: 177,172.51

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,416 : 121,569 = 121,569 : x
  2. Step 2: Convert to fraction form
    83,416/121,569 = 121,569/x
  3. Step 3: Cross multiply
    83,416x = 121,569 × 121,569
  4. Step 4: Simplify right side
    83,416x = 14,779,021,761
  5. Step 5: Solve for x
    x = 14,779,021,761/83,416
  6. Step 6: Final answer
    x = 177,172.51

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Why These Related Problems?

These problems maintain the same ratio (1.46) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.