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Finding the Third Proportional to 1,680 and 3,584

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Solution

The third proportional to 1,680 and 3,584 is: 7,645.87

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,680 : 3,584 = 3,584 : x
  2. Step 2: Convert to fraction form
    1,680/3,584 = 3,584/x
  3. Step 3: Cross multiply
    1,680x = 3,584 × 3,584
  4. Step 4: Simplify right side
    1,680x = 12,845,056
  5. Step 5: Solve for x
    x = 12,845,056/1,680
  6. Step 6: Final answer
    x = 7,645.87

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Why These Related Problems?

These problems maintain the same ratio (2.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.