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Finding the Third Proportional to 564.47 and 1,214.16

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Solution

The third proportional to 564.47 and 1,214.16 is: 2,611.62

Step by Step Solution

  1. Step 1: Write the proportion equation
    564.47 : 1,214.16 = 1,214.16 : x
  2. Step 2: Convert to fraction form
    564.47/1,214.16 = 1,214.16/x
  3. Step 3: Cross multiply
    564.47x = 1,214.16 × 1,214.16
  4. Step 4: Simplify right side
    564.47x = 1,474,175.40
  5. Step 5: Solve for x
    x = 1,474,175.40/564.47
  6. Step 6: Final answer
    x = 2,611.62

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Why These Related Problems?

These problems maintain the same ratio (2.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.