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Finding the Third Proportional to 301,411 and 410,470

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Solution

The third proportional to 301,411 and 410,470 is: 558,989.62

Step by Step Solution

  1. Step 1: Write the proportion equation
    301,411 : 410,470 = 410,470 : x
  2. Step 2: Convert to fraction form
    301,411/410,470 = 410,470/x
  3. Step 3: Cross multiply
    301,411x = 410,470 × 410,470
  4. Step 4: Simplify right side
    301,411x = 168,485,620,900
  5. Step 5: Solve for x
    x = 168,485,620,900/301,411
  6. Step 6: Final answer
    x = 558,989.62

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Why These Related Problems?

These problems maintain the same ratio (1.36) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.