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Finding the Third Proportional to 29,770 and 40,429

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Solution

The third proportional to 29,770 and 40,429 is: 54,904.40

Step by Step Solution

  1. Step 1: Write the proportion equation
    29,770 : 40,429 = 40,429 : x
  2. Step 2: Convert to fraction form
    29,770/40,429 = 40,429/x
  3. Step 3: Cross multiply
    29,770x = 40,429 × 40,429
  4. Step 4: Simplify right side
    29,770x = 1,634,504,041
  5. Step 5: Solve for x
    x = 1,634,504,041/29,770
  6. Step 6: Final answer
    x = 54,904.40

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Why These Related Problems?

These problems maintain the same ratio (1.36) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.