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Finding the Third Proportional to 2,380 and 5,120

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Solution

The third proportional to 2,380 and 5,120 is: 11,014.45

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,380 : 5,120 = 5,120 : x
  2. Step 2: Convert to fraction form
    2,380/5,120 = 5,120/x
  3. Step 3: Cross multiply
    2,380x = 5,120 × 5,120
  4. Step 4: Simplify right side
    2,380x = 26,214,400
  5. Step 5: Solve for x
    x = 26,214,400/2,380
  6. Step 6: Final answer
    x = 11,014.45

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Why These Related Problems?

These problems maintain the same ratio (2.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.