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Finding the Third Proportional to 7,742 and 12,354

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Solution

The third proportional to 7,742 and 12,354 is: 19,713.42

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,742 : 12,354 = 12,354 : x
  2. Step 2: Convert to fraction form
    7,742/12,354 = 12,354/x
  3. Step 3: Cross multiply
    7,742x = 12,354 × 12,354
  4. Step 4: Simplify right side
    7,742x = 152,621,316
  5. Step 5: Solve for x
    x = 152,621,316/7,742
  6. Step 6: Final answer
    x = 19,713.42

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Why These Related Problems?

These problems maintain the same ratio (1.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.