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Finding the Third Proportional to 8,209 and 17,585

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Solution

The third proportional to 8,209 and 17,585 is: 37,669.90

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,209 : 17,585 = 17,585 : x
  2. Step 2: Convert to fraction form
    8,209/17,585 = 17,585/x
  3. Step 3: Cross multiply
    8,209x = 17,585 × 17,585
  4. Step 4: Simplify right side
    8,209x = 309,232,225
  5. Step 5: Solve for x
    x = 309,232,225/8,209
  6. Step 6: Final answer
    x = 37,669.90

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.