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Finding the Third Proportional to 32,297 and 69,541

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Solution

The third proportional to 32,297 and 69,541 is: 149,733.74

Step by Step Solution

  1. Step 1: Write the proportion equation
    32,297 : 69,541 = 69,541 : x
  2. Step 2: Convert to fraction form
    32,297/69,541 = 69,541/x
  3. Step 3: Cross multiply
    32,297x = 69,541 × 69,541
  4. Step 4: Simplify right side
    32,297x = 4,835,950,681
  5. Step 5: Solve for x
    x = 4,835,950,681/32,297
  6. Step 6: Final answer
    x = 149,733.74

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Why These Related Problems?

These problems maintain the same ratio (2.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.