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Finding the Third Proportional to 1,972 and 5,194

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Solution

The third proportional to 1,972 and 5,194 is: 13,680.34

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,972 : 5,194 = 5,194 : x
  2. Step 2: Convert to fraction form
    1,972/5,194 = 5,194/x
  3. Step 3: Cross multiply
    1,972x = 5,194 × 5,194
  4. Step 4: Simplify right side
    1,972x = 26,977,636
  5. Step 5: Solve for x
    x = 26,977,636/1,972
  6. Step 6: Final answer
    x = 13,680.34

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Why These Related Problems?

These problems maintain the same ratio (2.63) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.