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Finding the Third Proportional to 1,542 and 2,097

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Solution

The third proportional to 1,542 and 2,097 is: 2,851.76

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,542 : 2,097 = 2,097 : x
  2. Step 2: Convert to fraction form
    1,542/2,097 = 2,097/x
  3. Step 3: Cross multiply
    1,542x = 2,097 × 2,097
  4. Step 4: Simplify right side
    1,542x = 4,397,409
  5. Step 5: Solve for x
    x = 4,397,409/1,542
  6. Step 6: Final answer
    x = 2,851.76

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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.