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Finding the Third Proportional to 1,540 and 2,091

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Solution

The third proportional to 1,540 and 2,091 is: 2,839.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,540 : 2,091 = 2,091 : x
  2. Step 2: Convert to fraction form
    1,540/2,091 = 2,091/x
  3. Step 3: Cross multiply
    1,540x = 2,091 × 2,091
  4. Step 4: Simplify right side
    1,540x = 4,372,281
  5. Step 5: Solve for x
    x = 4,372,281/1,540
  6. Step 6: Final answer
    x = 2,839.14

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Why These Related Problems?

These problems maintain the same ratio (1.36) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.