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Finding the Third Proportional to 310.75 and 412.13

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Solution

The third proportional to 310.75 and 412.13 is: 546.57

Step by Step Solution

  1. Step 1: Write the proportion equation
    310.75 : 412.13 = 412.13 : x
  2. Step 2: Convert to fraction form
    310.75/412.13 = 412.13/x
  3. Step 3: Cross multiply
    310.75x = 412.13 × 412.13
  4. Step 4: Simplify right side
    310.75x = 169,847.02
  5. Step 5: Solve for x
    x = 169,847.02/310.75
  6. Step 6: Final answer
    x = 546.57

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Why These Related Problems?

These problems maintain the same ratio (1.33) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.