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Finding the Third Proportional to 30,414 and 65,964

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Solution

The third proportional to 30,414 and 65,964 is: 143,067.31

Step by Step Solution

  1. Step 1: Write the proportion equation
    30,414 : 65,964 = 65,964 : x
  2. Step 2: Convert to fraction form
    30,414/65,964 = 65,964/x
  3. Step 3: Cross multiply
    30,414x = 65,964 × 65,964
  4. Step 4: Simplify right side
    30,414x = 4,351,249,296
  5. Step 5: Solve for x
    x = 4,351,249,296/30,414
  6. Step 6: Final answer
    x = 143,067.31

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.