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Finding the Third Proportional to 27,569 and 32,429

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Solution

The third proportional to 27,569 and 32,429 is: 38,145.74

Step by Step Solution

  1. Step 1: Write the proportion equation
    27,569 : 32,429 = 32,429 : x
  2. Step 2: Convert to fraction form
    27,569/32,429 = 32,429/x
  3. Step 3: Cross multiply
    27,569x = 32,429 × 32,429
  4. Step 4: Simplify right side
    27,569x = 1,051,640,041
  5. Step 5: Solve for x
    x = 1,051,640,041/27,569
  6. Step 6: Final answer
    x = 38,145.74

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Why These Related Problems?

These problems maintain the same ratio (1.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.