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Finding the Third Proportional to 209,748 and 296,509

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Solution

The third proportional to 209,748 and 296,509 is: 419,158.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    209,748 : 296,509 = 296,509 : x
  2. Step 2: Convert to fraction form
    209,748/296,509 = 296,509/x
  3. Step 3: Cross multiply
    209,748x = 296,509 × 296,509
  4. Step 4: Simplify right side
    209,748x = 87,917,587,081
  5. Step 5: Solve for x
    x = 87,917,587,081/209,748
  6. Step 6: Final answer
    x = 419,158.17

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Why These Related Problems?

These problems maintain the same ratio (1.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.