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Finding the Third Proportional to 591 and 1,274

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Solution

The third proportional to 591 and 1,274 is: 2,746.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    591 : 1,274 = 1,274 : x
  2. Step 2: Convert to fraction form
    591/1,274 = 1,274/x
  3. Step 3: Cross multiply
    591x = 1,274 × 1,274
  4. Step 4: Simplify right side
    591x = 1,623,076
  5. Step 5: Solve for x
    x = 1,623,076/591
  6. Step 6: Final answer
    x = 2,746.32

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.