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Finding the Third Proportional to 2,585 and 5,659

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Solution

The third proportional to 2,585 and 5,659 is: 12,388.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,585 : 5,659 = 5,659 : x
  2. Step 2: Convert to fraction form
    2,585/5,659 = 5,659/x
  3. Step 3: Cross multiply
    2,585x = 5,659 × 5,659
  4. Step 4: Simplify right side
    2,585x = 32,024,281
  5. Step 5: Solve for x
    x = 32,024,281/2,585
  6. Step 6: Final answer
    x = 12,388.50

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.