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Finding the Third Proportional to 120,420 and 257,514

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Solution

The third proportional to 120,420 and 257,514 is: 550,684.77

Step by Step Solution

  1. Step 1: Write the proportion equation
    120,420 : 257,514 = 257,514 : x
  2. Step 2: Convert to fraction form
    120,420/257,514 = 257,514/x
  3. Step 3: Cross multiply
    120,420x = 257,514 × 257,514
  4. Step 4: Simplify right side
    120,420x = 66,313,460,196
  5. Step 5: Solve for x
    x = 66,313,460,196/120,420
  6. Step 6: Final answer
    x = 550,684.77

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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.