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Finding the Third Proportional to 282,365 and 414,128

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Solution

The third proportional to 282,365 and 414,128 is: 607,376.98

Step by Step Solution

  1. Step 1: Write the proportion equation
    282,365 : 414,128 = 414,128 : x
  2. Step 2: Convert to fraction form
    282,365/414,128 = 414,128/x
  3. Step 3: Cross multiply
    282,365x = 414,128 × 414,128
  4. Step 4: Simplify right side
    282,365x = 171,502,000,384
  5. Step 5: Solve for x
    x = 171,502,000,384/282,365
  6. Step 6: Final answer
    x = 607,376.98

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.