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Finding the Third Proportional to 691 and 1,540

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Solution

The third proportional to 691 and 1,540 is: 3,432.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    691 : 1,540 = 1,540 : x
  2. Step 2: Convert to fraction form
    691/1,540 = 1,540/x
  3. Step 3: Cross multiply
    691x = 1,540 × 1,540
  4. Step 4: Simplify right side
    691x = 2,371,600
  5. Step 5: Solve for x
    x = 2,371,600/691
  6. Step 6: Final answer
    x = 3,432.13

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Why These Related Problems?

These problems maintain the same ratio (2.23) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.