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Finding the Third Proportional to 32,454 and 69,972

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Solution

The third proportional to 32,454 and 69,972 is: 150,862.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    32,454 : 69,972 = 69,972 : x
  2. Step 2: Convert to fraction form
    32,454/69,972 = 69,972/x
  3. Step 3: Cross multiply
    32,454x = 69,972 × 69,972
  4. Step 4: Simplify right side
    32,454x = 4,896,080,784
  5. Step 5: Solve for x
    x = 4,896,080,784/32,454
  6. Step 6: Final answer
    x = 150,862.17

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.