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Finding the Third Proportional to 5,740 and 8,454

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Solution

The third proportional to 5,740 and 8,454 is: 12,451.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,740 : 8,454 = 8,454 : x
  2. Step 2: Convert to fraction form
    5,740/8,454 = 8,454/x
  3. Step 3: Cross multiply
    5,740x = 8,454 × 8,454
  4. Step 4: Simplify right side
    5,740x = 71,470,116
  5. Step 5: Solve for x
    x = 71,470,116/5,740
  6. Step 6: Final answer
    x = 12,451.24

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.