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Finding the Third Proportional to 407 and 457.50

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Solution

The third proportional to 407 and 457.50 is: 514.27

Step by Step Solution

  1. Step 1: Write the proportion equation
    407 : 457.50 = 457.50 : x
  2. Step 2: Convert to fraction form
    407/457.50 = 457.50/x
  3. Step 3: Cross multiply
    407x = 457.50 × 457.50
  4. Step 4: Simplify right side
    407x = 209,306.25
  5. Step 5: Solve for x
    x = 209,306.25/407
  6. Step 6: Final answer
    x = 514.27

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Why These Related Problems?

These problems maintain the same ratio (1.12) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.