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Finding the Third Proportional to 412.88 and 542.25

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Solution

The third proportional to 412.88 and 542.25 is: 712.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    412.88 : 542.25 = 542.25 : x
  2. Step 2: Convert to fraction form
    412.88/542.25 = 542.25/x
  3. Step 3: Cross multiply
    412.88x = 542.25 × 542.25
  4. Step 4: Simplify right side
    412.88x = 294,035.06
  5. Step 5: Solve for x
    x = 294,035.06/412.88
  6. Step 6: Final answer
    x = 712.16

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Why These Related Problems?

These problems maintain the same ratio (1.31) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.