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Finding the Third Proportional to 51,840 and 77,742

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Solution

The third proportional to 51,840 and 77,742 is: 116,586.01

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,840 : 77,742 = 77,742 : x
  2. Step 2: Convert to fraction form
    51,840/77,742 = 77,742/x
  3. Step 3: Cross multiply
    51,840x = 77,742 × 77,742
  4. Step 4: Simplify right side
    51,840x = 6,043,818,564
  5. Step 5: Solve for x
    x = 6,043,818,564/51,840
  6. Step 6: Final answer
    x = 116,586.01

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.