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Finding the Third Proportional to 284.06 and 419.34

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Solution

The third proportional to 284.06 and 419.34 is: 619.05

Step by Step Solution

  1. Step 1: Write the proportion equation
    284.06 : 419.34 = 419.34 : x
  2. Step 2: Convert to fraction form
    284.06/419.34 = 419.34/x
  3. Step 3: Cross multiply
    284.06x = 419.34 × 419.34
  4. Step 4: Simplify right side
    284.06x = 175,849.18
  5. Step 5: Solve for x
    x = 175,849.18/284.06
  6. Step 6: Final answer
    x = 619.05

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Why These Related Problems?

These problems maintain the same ratio (1.48) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.