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Finding the Third Proportional to 1,542 and 1,743

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Solution

The third proportional to 1,542 and 1,743 is: 1,970.20

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,542 : 1,743 = 1,743 : x
  2. Step 2: Convert to fraction form
    1,542/1,743 = 1,743/x
  3. Step 3: Cross multiply
    1,542x = 1,743 × 1,743
  4. Step 4: Simplify right side
    1,542x = 3,038,049
  5. Step 5: Solve for x
    x = 3,038,049/1,542
  6. Step 6: Final answer
    x = 1,970.20

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Why These Related Problems?

These problems maintain the same ratio (1.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.