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Finding the Third Proportional to 7,782 and 14,322

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Solution

The third proportional to 7,782 and 14,322 is: 26,358.22

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,782 : 14,322 = 14,322 : x
  2. Step 2: Convert to fraction form
    7,782/14,322 = 14,322/x
  3. Step 3: Cross multiply
    7,782x = 14,322 × 14,322
  4. Step 4: Simplify right side
    7,782x = 205,119,684
  5. Step 5: Solve for x
    x = 205,119,684/7,782
  6. Step 6: Final answer
    x = 26,358.22

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Why These Related Problems?

These problems maintain the same ratio (1.84) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.