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Finding the Third Proportional to 4,194 and 6,142

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Solution

The third proportional to 4,194 and 6,142 is: 8,994.79

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,194 : 6,142 = 6,142 : x
  2. Step 2: Convert to fraction form
    4,194/6,142 = 6,142/x
  3. Step 3: Cross multiply
    4,194x = 6,142 × 6,142
  4. Step 4: Simplify right side
    4,194x = 37,724,164
  5. Step 5: Solve for x
    x = 37,724,164/4,194
  6. Step 6: Final answer
    x = 8,994.79

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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.