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Finding the Third Proportional to 412.13 and 569.06

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Solution

The third proportional to 412.13 and 569.06 is: 785.76

Step by Step Solution

  1. Step 1: Write the proportion equation
    412.13 : 569.06 = 569.06 : x
  2. Step 2: Convert to fraction form
    412.13/569.06 = 569.06/x
  3. Step 3: Cross multiply
    412.13x = 569.06 × 569.06
  4. Step 4: Simplify right side
    412.13x = 323,832.13
  5. Step 5: Solve for x
    x = 323,832.13/412.13
  6. Step 6: Final answer
    x = 785.76

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Why These Related Problems?

These problems maintain the same ratio (1.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.