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Finding the Third Proportional to 523 and 823.50

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Solution

The third proportional to 523 and 823.50 is: 1,296.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    523 : 823.50 = 823.50 : x
  2. Step 2: Convert to fraction form
    523/823.50 = 823.50/x
  3. Step 3: Cross multiply
    523x = 823.50 × 823.50
  4. Step 4: Simplify right side
    523x = 678,152.25
  5. Step 5: Solve for x
    x = 678,152.25/523
  6. Step 6: Final answer
    x = 1,296.66

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.