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Finding the Third Proportional to 82,521 and 180,498

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Solution

The third proportional to 82,521 and 180,498 is: 394,802.87

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,521 : 180,498 = 180,498 : x
  2. Step 2: Convert to fraction form
    82,521/180,498 = 180,498/x
  3. Step 3: Cross multiply
    82,521x = 180,498 × 180,498
  4. Step 4: Simplify right side
    82,521x = 32,579,528,004
  5. Step 5: Solve for x
    x = 32,579,528,004/82,521
  6. Step 6: Final answer
    x = 394,802.87

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.