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Finding the Third Proportional to 523 and 731.50

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Solution

The third proportional to 523 and 731.50 is: 1,023.12

Step by Step Solution

  1. Step 1: Write the proportion equation
    523 : 731.50 = 731.50 : x
  2. Step 2: Convert to fraction form
    523/731.50 = 731.50/x
  3. Step 3: Cross multiply
    523x = 731.50 × 731.50
  4. Step 4: Simplify right side
    523x = 535,092.25
  5. Step 5: Solve for x
    x = 535,092.25/523
  6. Step 6: Final answer
    x = 1,023.12

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Why These Related Problems?

These problems maintain the same ratio (1.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.