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Finding the Third Proportional to 523,384 and 830,102

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Solution

The third proportional to 523,384 and 830,102 is: 1,316,565.52

Step by Step Solution

  1. Step 1: Write the proportion equation
    523,384 : 830,102 = 830,102 : x
  2. Step 2: Convert to fraction form
    523,384/830,102 = 830,102/x
  3. Step 3: Cross multiply
    523,384x = 830,102 × 830,102
  4. Step 4: Simplify right side
    523,384x = 689,069,330,404
  5. Step 5: Solve for x
    x = 689,069,330,404/523,384
  6. Step 6: Final answer
    x = 1,316,565.52

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.