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Finding the Third Proportional to 6,502 and 7,690

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Solution

The third proportional to 6,502 and 7,690 is: 9,095.06

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,502 : 7,690 = 7,690 : x
  2. Step 2: Convert to fraction form
    6,502/7,690 = 7,690/x
  3. Step 3: Cross multiply
    6,502x = 7,690 × 7,690
  4. Step 4: Simplify right side
    6,502x = 59,136,100
  5. Step 5: Solve for x
    x = 59,136,100/6,502
  6. Step 6: Final answer
    x = 9,095.06

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Why These Related Problems?

These problems maintain the same ratio (1.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.