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Finding the Third Proportional to 180,120 and 417,009

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Solution

The third proportional to 180,120 and 417,009 is: 965,448.07

Step by Step Solution

  1. Step 1: Write the proportion equation
    180,120 : 417,009 = 417,009 : x
  2. Step 2: Convert to fraction form
    180,120/417,009 = 417,009/x
  3. Step 3: Cross multiply
    180,120x = 417,009 × 417,009
  4. Step 4: Simplify right side
    180,120x = 173,896,506,081
  5. Step 5: Solve for x
    x = 173,896,506,081/180,120
  6. Step 6: Final answer
    x = 965,448.07

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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.