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Finding the Third Proportional to 106,416 and 232,776

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Solution

The third proportional to 106,416 and 232,776 is: 509,177.81

Step by Step Solution

  1. Step 1: Write the proportion equation
    106,416 : 232,776 = 232,776 : x
  2. Step 2: Convert to fraction form
    106,416/232,776 = 232,776/x
  3. Step 3: Cross multiply
    106,416x = 232,776 × 232,776
  4. Step 4: Simplify right side
    106,416x = 54,184,666,176
  5. Step 5: Solve for x
    x = 54,184,666,176/106,416
  6. Step 6: Final answer
    x = 509,177.81

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.