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Finding the Third Proportional to 420.75 and 457.88

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Solution

The third proportional to 420.75 and 457.88 is: 498.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    420.75 : 457.88 = 457.88 : x
  2. Step 2: Convert to fraction form
    420.75/457.88 = 457.88/x
  3. Step 3: Cross multiply
    420.75x = 457.88 × 457.88
  4. Step 4: Simplify right side
    420.75x = 209,649.52
  5. Step 5: Solve for x
    x = 209,649.52/420.75
  6. Step 6: Final answer
    x = 498.28

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Why These Related Problems?

These problems maintain the same ratio (1.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.