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Finding the Third Proportional to 102,072 and 149,646

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Solution

The third proportional to 102,072 and 149,646 is: 219,393.42

Step by Step Solution

  1. Step 1: Write the proportion equation
    102,072 : 149,646 = 149,646 : x
  2. Step 2: Convert to fraction form
    102,072/149,646 = 149,646/x
  3. Step 3: Cross multiply
    102,072x = 149,646 × 149,646
  4. Step 4: Simplify right side
    102,072x = 22,393,925,316
  5. Step 5: Solve for x
    x = 22,393,925,316/102,072
  6. Step 6: Final answer
    x = 219,393.42

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.