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Finding the Third Proportional to 282,102 and 412,342

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Solution

The third proportional to 282,102 and 412,342 is: 602,710.81

Step by Step Solution

  1. Step 1: Write the proportion equation
    282,102 : 412,342 = 412,342 : x
  2. Step 2: Convert to fraction form
    282,102/412,342 = 412,342/x
  3. Step 3: Cross multiply
    282,102x = 412,342 × 412,342
  4. Step 4: Simplify right side
    282,102x = 170,025,924,964
  5. Step 5: Solve for x
    x = 170,025,924,964/282,102
  6. Step 6: Final answer
    x = 602,710.81

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Why These Related Problems?

These problems maintain the same ratio (1.46) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.