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Finding the Third Proportional to 6,506 and 7,850

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Solution

The third proportional to 6,506 and 7,850 is: 9,471.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,506 : 7,850 = 7,850 : x
  2. Step 2: Convert to fraction form
    6,506/7,850 = 7,850/x
  3. Step 3: Cross multiply
    6,506x = 7,850 × 7,850
  4. Step 4: Simplify right side
    6,506x = 61,622,500
  5. Step 5: Solve for x
    x = 61,622,500/6,506
  6. Step 6: Final answer
    x = 9,471.64

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Why These Related Problems?

These problems maintain the same ratio (1.21) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.