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Finding the Third Proportional to 677 and 1,677.50

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Solution

The third proportional to 677 and 1,677.50 is: 4,156.58

Step by Step Solution

  1. Step 1: Write the proportion equation
    677 : 1,677.50 = 1,677.50 : x
  2. Step 2: Convert to fraction form
    677/1,677.50 = 1,677.50/x
  3. Step 3: Cross multiply
    677x = 1,677.50 × 1,677.50
  4. Step 4: Simplify right side
    677x = 2,814,006.25
  5. Step 5: Solve for x
    x = 2,814,006.25/677
  6. Step 6: Final answer
    x = 4,156.58

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Why These Related Problems?

These problems maintain the same ratio (2.48) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.