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Finding the Third Proportional to 13,677 and 32,205

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Solution

The third proportional to 13,677 and 32,205 is: 75,832.57

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,677 : 32,205 = 32,205 : x
  2. Step 2: Convert to fraction form
    13,677/32,205 = 32,205/x
  3. Step 3: Cross multiply
    13,677x = 32,205 × 32,205
  4. Step 4: Simplify right side
    13,677x = 1,037,162,025
  5. Step 5: Solve for x
    x = 1,037,162,025/13,677
  6. Step 6: Final answer
    x = 75,832.57

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Why These Related Problems?

These problems maintain the same ratio (2.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.