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Finding the Third Proportional to 523,511 and 830,304

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Solution

The third proportional to 523,511 and 830,304 is: 1,316,886.81

Step by Step Solution

  1. Step 1: Write the proportion equation
    523,511 : 830,304 = 830,304 : x
  2. Step 2: Convert to fraction form
    523,511/830,304 = 830,304/x
  3. Step 3: Cross multiply
    523,511x = 830,304 × 830,304
  4. Step 4: Simplify right side
    523,511x = 689,404,732,416
  5. Step 5: Solve for x
    x = 689,404,732,416/523,511
  6. Step 6: Final answer
    x = 1,316,886.81

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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.