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Finding the Third Proportional to 51,023 and 108,223

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Solution

The third proportional to 51,023 and 108,223 is: 229,547.81

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,023 : 108,223 = 108,223 : x
  2. Step 2: Convert to fraction form
    51,023/108,223 = 108,223/x
  3. Step 3: Cross multiply
    51,023x = 108,223 × 108,223
  4. Step 4: Simplify right side
    51,023x = 11,712,217,729
  5. Step 5: Solve for x
    x = 11,712,217,729/51,023
  6. Step 6: Final answer
    x = 229,547.81

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Why These Related Problems?

These problems maintain the same ratio (2.12) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.