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Finding the Third Proportional to 261,824 and 409,584

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Solution

The third proportional to 261,824 and 409,584 is: 640,732.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    261,824 : 409,584 = 409,584 : x
  2. Step 2: Convert to fraction form
    261,824/409,584 = 409,584/x
  3. Step 3: Cross multiply
    261,824x = 409,584 × 409,584
  4. Step 4: Simplify right side
    261,824x = 167,759,053,056
  5. Step 5: Solve for x
    x = 167,759,053,056/261,824
  6. Step 6: Final answer
    x = 640,732.14

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Why These Related Problems?

These problems maintain the same ratio (1.56) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.