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Finding the Third Proportional to 209,165 and 314,224

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Solution

The third proportional to 209,165 and 314,224 is: 472,051.84

Step by Step Solution

  1. Step 1: Write the proportion equation
    209,165 : 314,224 = 314,224 : x
  2. Step 2: Convert to fraction form
    209,165/314,224 = 314,224/x
  3. Step 3: Cross multiply
    209,165x = 314,224 × 314,224
  4. Step 4: Simplify right side
    209,165x = 98,736,722,176
  5. Step 5: Solve for x
    x = 98,736,722,176/209,165
  6. Step 6: Final answer
    x = 472,051.84

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.