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Finding the Third Proportional to 257,698 and 409,971

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Solution

The third proportional to 257,698 and 409,971 is: 652,221.67

Step by Step Solution

  1. Step 1: Write the proportion equation
    257,698 : 409,971 = 409,971 : x
  2. Step 2: Convert to fraction form
    257,698/409,971 = 409,971/x
  3. Step 3: Cross multiply
    257,698x = 409,971 × 409,971
  4. Step 4: Simplify right side
    257,698x = 168,076,220,841
  5. Step 5: Solve for x
    x = 168,076,220,841/257,698
  6. Step 6: Final answer
    x = 652,221.67

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.