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Finding the Third Proportional to 7,838 and 14,566

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Solution

The third proportional to 7,838 and 14,566 is: 27,069.20

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,838 : 14,566 = 14,566 : x
  2. Step 2: Convert to fraction form
    7,838/14,566 = 14,566/x
  3. Step 3: Cross multiply
    7,838x = 14,566 × 14,566
  4. Step 4: Simplify right side
    7,838x = 212,168,356
  5. Step 5: Solve for x
    x = 212,168,356/7,838
  6. Step 6: Final answer
    x = 27,069.20

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Why These Related Problems?

These problems maintain the same ratio (1.86) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.