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Finding the Third Proportional to 782.50 and 1,605.50

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Solution

The third proportional to 782.50 and 1,605.50 is: 3,294.10

Step by Step Solution

  1. Step 1: Write the proportion equation
    782.50 : 1,605.50 = 1,605.50 : x
  2. Step 2: Convert to fraction form
    782.50/1,605.50 = 1,605.50/x
  3. Step 3: Cross multiply
    782.50x = 1,605.50 × 1,605.50
  4. Step 4: Simplify right side
    782.50x = 2,577,630.25
  5. Step 5: Solve for x
    x = 2,577,630.25/782.50
  6. Step 6: Final answer
    x = 3,294.10

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Why These Related Problems?

These problems maintain the same ratio (2.05) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.