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Finding the Third Proportional to 314,342 and 643,210

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Solution

The third proportional to 314,342 and 643,210 is: 1,316,143.26

Step by Step Solution

  1. Step 1: Write the proportion equation
    314,342 : 643,210 = 643,210 : x
  2. Step 2: Convert to fraction form
    314,342/643,210 = 643,210/x
  3. Step 3: Cross multiply
    314,342x = 643,210 × 643,210
  4. Step 4: Simplify right side
    314,342x = 413,719,104,100
  5. Step 5: Solve for x
    x = 413,719,104,100/314,342
  6. Step 6: Final answer
    x = 1,316,143.26

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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.