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Finding the Third Proportional to 2,586 and 2,784

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Solution

The third proportional to 2,586 and 2,784 is: 2,997.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,586 : 2,784 = 2,784 : x
  2. Step 2: Convert to fraction form
    2,586/2,784 = 2,784/x
  3. Step 3: Cross multiply
    2,586x = 2,784 × 2,784
  4. Step 4: Simplify right side
    2,586x = 7,750,656
  5. Step 5: Solve for x
    x = 7,750,656/2,586
  6. Step 6: Final answer
    x = 2,997.16

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Why These Related Problems?

These problems maintain the same ratio (1.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.