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Finding the Third Proportional to 7,840 and 15,424

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Solution

The third proportional to 7,840 and 15,424 is: 30,344.36

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,840 : 15,424 = 15,424 : x
  2. Step 2: Convert to fraction form
    7,840/15,424 = 15,424/x
  3. Step 3: Cross multiply
    7,840x = 15,424 × 15,424
  4. Step 4: Simplify right side
    7,840x = 237,899,776
  5. Step 5: Solve for x
    x = 237,899,776/7,840
  6. Step 6: Final answer
    x = 30,344.36

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Why These Related Problems?

These problems maintain the same ratio (1.97) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.