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Finding the Third Proportional to 178,106 and 277,011

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Solution

The third proportional to 178,106 and 277,011 is: 430,839.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    178,106 : 277,011 = 277,011 : x
  2. Step 2: Convert to fraction form
    178,106/277,011 = 277,011/x
  3. Step 3: Cross multiply
    178,106x = 277,011 × 277,011
  4. Step 4: Simplify right side
    178,106x = 76,735,094,121
  5. Step 5: Solve for x
    x = 76,735,094,121/178,106
  6. Step 6: Final answer
    x = 430,839.47

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Why These Related Problems?

These problems maintain the same ratio (1.56) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.