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Finding the Third Proportional to 829.83 and 1,077.47

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Solution

The third proportional to 829.83 and 1,077.47 is: 1,399.01

Step by Step Solution

  1. Step 1: Write the proportion equation
    829.83 : 1,077.47 = 1,077.47 : x
  2. Step 2: Convert to fraction form
    829.83/1,077.47 = 1,077.47/x
  3. Step 3: Cross multiply
    829.83x = 1,077.47 × 1,077.47
  4. Step 4: Simplify right side
    829.83x = 1,160,938.91
  5. Step 5: Solve for x
    x = 1,160,938.91/829.83
  6. Step 6: Final answer
    x = 1,399.01

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Why These Related Problems?

These problems maintain the same ratio (1.30) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.