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Finding the Third Proportional to 31,974 and 48,407

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Solution

The third proportional to 31,974 and 48,407 is: 73,285.72

Step by Step Solution

  1. Step 1: Write the proportion equation
    31,974 : 48,407 = 48,407 : x
  2. Step 2: Convert to fraction form
    31,974/48,407 = 48,407/x
  3. Step 3: Cross multiply
    31,974x = 48,407 × 48,407
  4. Step 4: Simplify right side
    31,974x = 2,343,237,649
  5. Step 5: Solve for x
    x = 2,343,237,649/31,974
  6. Step 6: Final answer
    x = 73,285.72

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.