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Finding the Third Proportional to 8,184 and 12,964

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Solution

The third proportional to 8,184 and 12,964 is: 20,535.84

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,184 : 12,964 = 12,964 : x
  2. Step 2: Convert to fraction form
    8,184/12,964 = 12,964/x
  3. Step 3: Cross multiply
    8,184x = 12,964 × 12,964
  4. Step 4: Simplify right side
    8,184x = 168,065,296
  5. Step 5: Solve for x
    x = 168,065,296/8,184
  6. Step 6: Final answer
    x = 20,535.84

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Why These Related Problems?

These problems maintain the same ratio (1.58) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.