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Finding the Third Proportional to 421,291 and 646,014

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Solution

The third proportional to 421,291 and 646,014 is: 990,607.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    421,291 : 646,014 = 646,014 : x
  2. Step 2: Convert to fraction form
    421,291/646,014 = 646,014/x
  3. Step 3: Cross multiply
    421,291x = 646,014 × 646,014
  4. Step 4: Simplify right side
    421,291x = 417,334,088,196
  5. Step 5: Solve for x
    x = 417,334,088,196/421,291
  6. Step 6: Final answer
    x = 990,607.65

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Why These Related Problems?

These problems maintain the same ratio (1.53) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.