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Finding the Third Proportional to 82,184 and 120,348

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Solution

The third proportional to 82,184 and 120,348 is: 176,234.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,184 : 120,348 = 120,348 : x
  2. Step 2: Convert to fraction form
    82,184/120,348 = 120,348/x
  3. Step 3: Cross multiply
    82,184x = 120,348 × 120,348
  4. Step 4: Simplify right side
    82,184x = 14,483,641,104
  5. Step 5: Solve for x
    x = 14,483,641,104/82,184
  6. Step 6: Final answer
    x = 176,234.32

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Why These Related Problems?

These problems maintain the same ratio (1.46) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.