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Finding the Third Proportional to 5,200 and 6,574

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Solution

The third proportional to 5,200 and 6,574 is: 8,311.05

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,200 : 6,574 = 6,574 : x
  2. Step 2: Convert to fraction form
    5,200/6,574 = 6,574/x
  3. Step 3: Cross multiply
    5,200x = 6,574 × 6,574
  4. Step 4: Simplify right side
    5,200x = 43,217,476
  5. Step 5: Solve for x
    x = 43,217,476/5,200
  6. Step 6: Final answer
    x = 8,311.05

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Why These Related Problems?

These problems maintain the same ratio (1.26) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.