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Finding the Third Proportional to 102,034 and 216,418

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Solution

The third proportional to 102,034 and 216,418 is: 459,030.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    102,034 : 216,418 = 216,418 : x
  2. Step 2: Convert to fraction form
    102,034/216,418 = 216,418/x
  3. Step 3: Cross multiply
    102,034x = 216,418 × 216,418
  4. Step 4: Simplify right side
    102,034x = 46,836,750,724
  5. Step 5: Solve for x
    x = 46,836,750,724/102,034
  6. Step 6: Final answer
    x = 459,030.82

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Why These Related Problems?

These problems maintain the same ratio (2.12) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.