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Finding the Third Proportional to 257,540 and 409,798

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Solution

The third proportional to 257,540 and 409,798 is: 652,071.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    257,540 : 409,798 = 409,798 : x
  2. Step 2: Convert to fraction form
    257,540/409,798 = 409,798/x
  3. Step 3: Cross multiply
    257,540x = 409,798 × 409,798
  4. Step 4: Simplify right side
    257,540x = 167,934,400,804
  5. Step 5: Solve for x
    x = 167,934,400,804/257,540
  6. Step 6: Final answer
    x = 652,071.14

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.