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Finding the Third Proportional to 7,142 and 9,478

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Solution

The third proportional to 7,142 and 9,478 is: 12,578.06

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,142 : 9,478 = 9,478 : x
  2. Step 2: Convert to fraction form
    7,142/9,478 = 9,478/x
  3. Step 3: Cross multiply
    7,142x = 9,478 × 9,478
  4. Step 4: Simplify right side
    7,142x = 89,832,484
  5. Step 5: Solve for x
    x = 89,832,484/7,142
  6. Step 6: Final answer
    x = 12,578.06

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Why These Related Problems?

These problems maintain the same ratio (1.33) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.