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Finding the Third Proportional to 38,402 and 83,984

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Solution

The third proportional to 38,402 and 83,984 is: 183,670.44

Step by Step Solution

  1. Step 1: Write the proportion equation
    38,402 : 83,984 = 83,984 : x
  2. Step 2: Convert to fraction form
    38,402/83,984 = 83,984/x
  3. Step 3: Cross multiply
    38,402x = 83,984 × 83,984
  4. Step 4: Simplify right side
    38,402x = 7,053,312,256
  5. Step 5: Solve for x
    x = 7,053,312,256/38,402
  6. Step 6: Final answer
    x = 183,670.44

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.