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Finding the Third Proportional to 295,684 and 463,216

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Solution

The third proportional to 295,684 and 463,216 is: 725,670.18

Step by Step Solution

  1. Step 1: Write the proportion equation
    295,684 : 463,216 = 463,216 : x
  2. Step 2: Convert to fraction form
    295,684/463,216 = 463,216/x
  3. Step 3: Cross multiply
    295,684x = 463,216 × 463,216
  4. Step 4: Simplify right side
    295,684x = 214,569,062,656
  5. Step 5: Solve for x
    x = 214,569,062,656/295,684
  6. Step 6: Final answer
    x = 725,670.18

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.