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Finding the Third Proportional to 6,457 and 7,078

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Solution

The third proportional to 6,457 and 7,078 is: 7,758.72

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,457 : 7,078 = 7,078 : x
  2. Step 2: Convert to fraction form
    6,457/7,078 = 7,078/x
  3. Step 3: Cross multiply
    6,457x = 7,078 × 7,078
  4. Step 4: Simplify right side
    6,457x = 50,098,084
  5. Step 5: Solve for x
    x = 50,098,084/6,457
  6. Step 6: Final answer
    x = 7,758.72

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.