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Finding the Third Proportional to 1,072 and 1,297

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Solution

The third proportional to 1,072 and 1,297 is: 1,569.22

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,072 : 1,297 = 1,297 : x
  2. Step 2: Convert to fraction form
    1,072/1,297 = 1,297/x
  3. Step 3: Cross multiply
    1,072x = 1,297 × 1,297
  4. Step 4: Simplify right side
    1,072x = 1,682,209
  5. Step 5: Solve for x
    x = 1,682,209/1,072
  6. Step 6: Final answer
    x = 1,569.22

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Why These Related Problems?

These problems maintain the same ratio (1.21) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.