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Finding the Third Proportional to 180,146 and 417,047

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Solution

The third proportional to 180,146 and 417,047 is: 965,484.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    180,146 : 417,047 = 417,047 : x
  2. Step 2: Convert to fraction form
    180,146/417,047 = 417,047/x
  3. Step 3: Cross multiply
    180,146x = 417,047 × 417,047
  4. Step 4: Simplify right side
    180,146x = 173,928,200,209
  5. Step 5: Solve for x
    x = 173,928,200,209/180,146
  6. Step 6: Final answer
    x = 965,484.66

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Why These Related Problems?

These problems maintain the same ratio (2.32) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.