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Finding the Third Proportional to 1,540 and 1,952

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Solution

The third proportional to 1,540 and 1,952 is: 2,474.22

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,540 : 1,952 = 1,952 : x
  2. Step 2: Convert to fraction form
    1,540/1,952 = 1,952/x
  3. Step 3: Cross multiply
    1,540x = 1,952 × 1,952
  4. Step 4: Simplify right side
    1,540x = 3,810,304
  5. Step 5: Solve for x
    x = 3,810,304/1,540
  6. Step 6: Final answer
    x = 2,474.22

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Why These Related Problems?

These problems maintain the same ratio (1.27) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.