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Finding the Third Proportional to 1,834 and 4,200

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Solution

The third proportional to 1,834 and 4,200 is: 9,618.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,834 : 4,200 = 4,200 : x
  2. Step 2: Convert to fraction form
    1,834/4,200 = 4,200/x
  3. Step 3: Cross multiply
    1,834x = 4,200 × 4,200
  4. Step 4: Simplify right side
    1,834x = 17,640,000
  5. Step 5: Solve for x
    x = 17,640,000/1,834
  6. Step 6: Final answer
    x = 9,618.32

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Why These Related Problems?

These problems maintain the same ratio (2.29) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.