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Finding the Third Proportional to 213,683 and 457,012

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Solution

The third proportional to 213,683 and 457,012 is: 977,429.03

Step by Step Solution

  1. Step 1: Write the proportion equation
    213,683 : 457,012 = 457,012 : x
  2. Step 2: Convert to fraction form
    213,683/457,012 = 457,012/x
  3. Step 3: Cross multiply
    213,683x = 457,012 × 457,012
  4. Step 4: Simplify right side
    213,683x = 208,859,968,144
  5. Step 5: Solve for x
    x = 208,859,968,144/213,683
  6. Step 6: Final answer
    x = 977,429.03

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.