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Finding the Third Proportional to 13,084 and 19,585

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Solution

The third proportional to 13,084 and 19,585 is: 29,316.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,084 : 19,585 = 19,585 : x
  2. Step 2: Convert to fraction form
    13,084/19,585 = 19,585/x
  3. Step 3: Cross multiply
    13,084x = 19,585 × 19,585
  4. Step 4: Simplify right side
    13,084x = 383,572,225
  5. Step 5: Solve for x
    x = 383,572,225/13,084
  6. Step 6: Final answer
    x = 29,316.13

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.