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Finding the Third Proportional to 213,438 and 465,513

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Solution

The third proportional to 213,438 and 465,513 is: 1,015,294.15

Step by Step Solution

  1. Step 1: Write the proportion equation
    213,438 : 465,513 = 465,513 : x
  2. Step 2: Convert to fraction form
    213,438/465,513 = 465,513/x
  3. Step 3: Cross multiply
    213,438x = 465,513 × 465,513
  4. Step 4: Simplify right side
    213,438x = 216,702,353,169
  5. Step 5: Solve for x
    x = 216,702,353,169/213,438
  6. Step 6: Final answer
    x = 1,015,294.15

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.