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Finding the Third Proportional to 6,500 and 14,312

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Solution

The third proportional to 6,500 and 14,312 is: 31,512.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,500 : 14,312 = 14,312 : x
  2. Step 2: Convert to fraction form
    6,500/14,312 = 14,312/x
  3. Step 3: Cross multiply
    6,500x = 14,312 × 14,312
  4. Step 4: Simplify right side
    6,500x = 204,833,344
  5. Step 5: Solve for x
    x = 204,833,344/6,500
  6. Step 6: Final answer
    x = 31,512.82

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Why These Related Problems?

These problems maintain the same ratio (2.20) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.