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Finding the Third Proportional to 305,738 and 463,224

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Solution

The third proportional to 305,738 and 463,224 is: 701,831.22

Step by Step Solution

  1. Step 1: Write the proportion equation
    305,738 : 463,224 = 463,224 : x
  2. Step 2: Convert to fraction form
    305,738/463,224 = 463,224/x
  3. Step 3: Cross multiply
    305,738x = 463,224 × 463,224
  4. Step 4: Simplify right side
    305,738x = 214,576,474,176
  5. Step 5: Solve for x
    x = 214,576,474,176/305,738
  6. Step 6: Final answer
    x = 701,831.22

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Why These Related Problems?

These problems maintain the same ratio (1.52) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.