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Finding the Third Proportional to 144,006 and 314,214

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Solution

The third proportional to 144,006 and 314,214 is: 685,599.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    144,006 : 314,214 = 314,214 : x
  2. Step 2: Convert to fraction form
    144,006/314,214 = 314,214/x
  3. Step 3: Cross multiply
    144,006x = 314,214 × 314,214
  4. Step 4: Simplify right side
    144,006x = 98,730,437,796
  5. Step 5: Solve for x
    x = 98,730,437,796/144,006
  6. Step 6: Final answer
    x = 685,599.47

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.