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Finding the Third Proportional to 5,946 and 13,827

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Solution

The third proportional to 5,946 and 13,827 is: 32,153.70

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,946 : 13,827 = 13,827 : x
  2. Step 2: Convert to fraction form
    5,946/13,827 = 13,827/x
  3. Step 3: Cross multiply
    5,946x = 13,827 × 13,827
  4. Step 4: Simplify right side
    5,946x = 191,185,929
  5. Step 5: Solve for x
    x = 191,185,929/5,946
  6. Step 6: Final answer
    x = 32,153.70

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Why These Related Problems?

These problems maintain the same ratio (2.33) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.