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Finding the Third Proportional to 145,947 and 314,409

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Solution

The third proportional to 145,947 and 314,409 is: 677,321.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    145,947 : 314,409 = 314,409 : x
  2. Step 2: Convert to fraction form
    145,947/314,409 = 314,409/x
  3. Step 3: Cross multiply
    145,947x = 314,409 × 314,409
  4. Step 4: Simplify right side
    145,947x = 98,853,019,281
  5. Step 5: Solve for x
    x = 98,853,019,281/145,947
  6. Step 6: Final answer
    x = 677,321.35

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Why These Related Problems?

These problems maintain the same ratio (2.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.