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Finding the Third Proportional to 10,780 and 14,557

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Solution

The third proportional to 10,780 and 14,557 is: 19,657.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,780 : 14,557 = 14,557 : x
  2. Step 2: Convert to fraction form
    10,780/14,557 = 14,557/x
  3. Step 3: Cross multiply
    10,780x = 14,557 × 14,557
  4. Step 4: Simplify right side
    10,780x = 211,906,249
  5. Step 5: Solve for x
    x = 211,906,249/10,780
  6. Step 6: Final answer
    x = 19,657.35

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Why These Related Problems?

These problems maintain the same ratio (1.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.