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Finding the Third Proportional to 5,200 and 6,746

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Solution

The third proportional to 5,200 and 6,746 is: 8,751.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,200 : 6,746 = 6,746 : x
  2. Step 2: Convert to fraction form
    5,200/6,746 = 6,746/x
  3. Step 3: Cross multiply
    5,200x = 6,746 × 6,746
  4. Step 4: Simplify right side
    5,200x = 45,508,516
  5. Step 5: Solve for x
    x = 45,508,516/5,200
  6. Step 6: Final answer
    x = 8,751.64

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Why These Related Problems?

These problems maintain the same ratio (1.30) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.