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Finding the Third Proportional to 7,457 and 8,267

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Solution

The third proportional to 7,457 and 8,267 is: 9,164.98

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,457 : 8,267 = 8,267 : x
  2. Step 2: Convert to fraction form
    7,457/8,267 = 8,267/x
  3. Step 3: Cross multiply
    7,457x = 8,267 × 8,267
  4. Step 4: Simplify right side
    7,457x = 68,343,289
  5. Step 5: Solve for x
    x = 68,343,289/7,457
  6. Step 6: Final answer
    x = 9,164.98

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Why These Related Problems?

These problems maintain the same ratio (1.11) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.