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Finding the Third Proportional to 214,567 and 456,854

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Solution

The third proportional to 214,567 and 456,854 is: 972,729.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    214,567 : 456,854 = 456,854 : x
  2. Step 2: Convert to fraction form
    214,567/456,854 = 456,854/x
  3. Step 3: Cross multiply
    214,567x = 456,854 × 456,854
  4. Step 4: Simplify right side
    214,567x = 208,715,577,316
  5. Step 5: Solve for x
    x = 208,715,577,316/214,567
  6. Step 6: Final answer
    x = 972,729.16

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Why These Related Problems?

These problems maintain the same ratio (2.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.