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Finding the Third Proportional to 105,991 and 159,213

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Solution

The third proportional to 105,991 and 159,213 is: 239,159.73

Step by Step Solution

  1. Step 1: Write the proportion equation
    105,991 : 159,213 = 159,213 : x
  2. Step 2: Convert to fraction form
    105,991/159,213 = 159,213/x
  3. Step 3: Cross multiply
    105,991x = 159,213 × 159,213
  4. Step 4: Simplify right side
    105,991x = 25,348,779,369
  5. Step 5: Solve for x
    x = 25,348,779,369/105,991
  6. Step 6: Final answer
    x = 239,159.73

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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.