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Finding the Third Proportional to 6,507 and 7,827

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Solution

The third proportional to 6,507 and 7,827 is: 9,414.77

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,507 : 7,827 = 7,827 : x
  2. Step 2: Convert to fraction form
    6,507/7,827 = 7,827/x
  3. Step 3: Cross multiply
    6,507x = 7,827 × 7,827
  4. Step 4: Simplify right side
    6,507x = 61,261,929
  5. Step 5: Solve for x
    x = 61,261,929/6,507
  6. Step 6: Final answer
    x = 9,414.77

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Why These Related Problems?

These problems maintain the same ratio (1.20) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.