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Finding the Third Proportional to 1,680 and 2,859

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Solution

The third proportional to 1,680 and 2,859 is: 4,865.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,680 : 2,859 = 2,859 : x
  2. Step 2: Convert to fraction form
    1,680/2,859 = 2,859/x
  3. Step 3: Cross multiply
    1,680x = 2,859 × 2,859
  4. Step 4: Simplify right side
    1,680x = 8,173,881
  5. Step 5: Solve for x
    x = 8,173,881/1,680
  6. Step 6: Final answer
    x = 4,865.41

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Why These Related Problems?

These problems maintain the same ratio (1.70) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.