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Finding the Third Proportional to 102,971 and 210,959

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Solution

The third proportional to 102,971 and 210,959 is: 432,196.44

Step by Step Solution

  1. Step 1: Write the proportion equation
    102,971 : 210,959 = 210,959 : x
  2. Step 2: Convert to fraction form
    102,971/210,959 = 210,959/x
  3. Step 3: Cross multiply
    102,971x = 210,959 × 210,959
  4. Step 4: Simplify right side
    102,971x = 44,503,699,681
  5. Step 5: Solve for x
    x = 44,503,699,681/102,971
  6. Step 6: Final answer
    x = 432,196.44

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Why These Related Problems?

These problems maintain the same ratio (2.05) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.