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Finding the Third Proportional to 19,504 and 31,409

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Solution

The third proportional to 19,504 and 31,409 is: 50,580.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    19,504 : 31,409 = 31,409 : x
  2. Step 2: Convert to fraction form
    19,504/31,409 = 31,409/x
  3. Step 3: Cross multiply
    19,504x = 31,409 × 31,409
  4. Step 4: Simplify right side
    19,504x = 986,525,281
  5. Step 5: Solve for x
    x = 986,525,281/19,504
  6. Step 6: Final answer
    x = 50,580.66

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Why These Related Problems?

These problems maintain the same ratio (1.61) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.