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Finding the Third Proportional to 524.25 and 1,414.13

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Solution

The third proportional to 524.25 and 1,414.13 is: 3,814.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    524.25 : 1,414.13 = 1,414.13 : x
  2. Step 2: Convert to fraction form
    524.25/1,414.13 = 1,414.13/x
  3. Step 3: Cross multiply
    524.25x = 1,414.13 × 1,414.13
  4. Step 4: Simplify right side
    524.25x = 1,999,749.52
  5. Step 5: Solve for x
    x = 1,999,749.52/524.25
  6. Step 6: Final answer
    x = 3,814.50

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Why These Related Problems?

These problems maintain the same ratio (2.70) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.