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Finding the Third Proportional to 14,566 and 16,078

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Solution

The third proportional to 14,566 and 16,078 is: 17,746.95

Step by Step Solution

  1. Step 1: Write the proportion equation
    14,566 : 16,078 = 16,078 : x
  2. Step 2: Convert to fraction form
    14,566/16,078 = 16,078/x
  3. Step 3: Cross multiply
    14,566x = 16,078 × 16,078
  4. Step 4: Simplify right side
    14,566x = 258,502,084
  5. Step 5: Solve for x
    x = 258,502,084/14,566
  6. Step 6: Final answer
    x = 17,746.95

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.