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Finding the Third Proportional to 385 and 419.50

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Solution

The third proportional to 385 and 419.50 is: 457.09

Step by Step Solution

  1. Step 1: Write the proportion equation
    385 : 419.50 = 419.50 : x
  2. Step 2: Convert to fraction form
    385/419.50 = 419.50/x
  3. Step 3: Cross multiply
    385x = 419.50 × 419.50
  4. Step 4: Simplify right side
    385x = 175,980.25
  5. Step 5: Solve for x
    x = 175,980.25/385
  6. Step 6: Final answer
    x = 457.09

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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.