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Finding the Third Proportional to 299,178 and 413,470

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Solution

The third proportional to 299,178 and 413,470 is: 571,423.84

Step by Step Solution

  1. Step 1: Write the proportion equation
    299,178 : 413,470 = 413,470 : x
  2. Step 2: Convert to fraction form
    299,178/413,470 = 413,470/x
  3. Step 3: Cross multiply
    299,178x = 413,470 × 413,470
  4. Step 4: Simplify right side
    299,178x = 170,957,440,900
  5. Step 5: Solve for x
    x = 170,957,440,900/299,178
  6. Step 6: Final answer
    x = 571,423.84

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Why These Related Problems?

These problems maintain the same ratio (1.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.