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Finding the Third Proportional to 781.50 and 1,643

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Solution

The third proportional to 781.50 and 1,643 is: 3,454.19

Step by Step Solution

  1. Step 1: Write the proportion equation
    781.50 : 1,643 = 1,643 : x
  2. Step 2: Convert to fraction form
    781.50/1,643 = 1,643/x
  3. Step 3: Cross multiply
    781.50x = 1,643 × 1,643
  4. Step 4: Simplify right side
    781.50x = 2,699,449
  5. Step 5: Solve for x
    x = 2,699,449/781.50
  6. Step 6: Final answer
    x = 3,454.19

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Why These Related Problems?

These problems maintain the same ratio (2.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.