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Finding the Third Proportional to 8,284 and 10,138

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Solution

The third proportional to 8,284 and 10,138 is: 12,406.93

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,284 : 10,138 = 10,138 : x
  2. Step 2: Convert to fraction form
    8,284/10,138 = 10,138/x
  3. Step 3: Cross multiply
    8,284x = 10,138 × 10,138
  4. Step 4: Simplify right side
    8,284x = 102,779,044
  5. Step 5: Solve for x
    x = 102,779,044/8,284
  6. Step 6: Final answer
    x = 12,406.93

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Why These Related Problems?

These problems maintain the same ratio (1.22) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.