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Finding the Third Proportional to 1,584 and 2,314

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Solution

The third proportional to 1,584 and 2,314 is: 3,380.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,584 : 2,314 = 2,314 : x
  2. Step 2: Convert to fraction form
    1,584/2,314 = 2,314/x
  3. Step 3: Cross multiply
    1,584x = 2,314 × 2,314
  4. Step 4: Simplify right side
    1,584x = 5,354,596
  5. Step 5: Solve for x
    x = 5,354,596/1,584
  6. Step 6: Final answer
    x = 3,380.43

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Why These Related Problems?

These problems maintain the same ratio (1.46) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.