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Finding the Third Proportional to 105,946 and 157,086

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Solution

The third proportional to 105,946 and 157,086 is: 232,911.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    105,946 : 157,086 = 157,086 : x
  2. Step 2: Convert to fraction form
    105,946/157,086 = 157,086/x
  3. Step 3: Cross multiply
    105,946x = 157,086 × 157,086
  4. Step 4: Simplify right side
    105,946x = 24,676,011,396
  5. Step 5: Solve for x
    x = 24,676,011,396/105,946
  6. Step 6: Final answer
    x = 232,911.21

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Why These Related Problems?

These problems maintain the same ratio (1.48) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.