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Finding the Third Proportional to 1,306 and 1,434

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Solution

The third proportional to 1,306 and 1,434 is: 1,574.55

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,306 : 1,434 = 1,434 : x
  2. Step 2: Convert to fraction form
    1,306/1,434 = 1,434/x
  3. Step 3: Cross multiply
    1,306x = 1,434 × 1,434
  4. Step 4: Simplify right side
    1,306x = 2,056,356
  5. Step 5: Solve for x
    x = 2,056,356/1,306
  6. Step 6: Final answer
    x = 1,574.55

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.