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Finding the Third Proportional to 30,496 and 65,984

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Solution

The third proportional to 30,496 and 65,984 is: 142,769.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    30,496 : 65,984 = 65,984 : x
  2. Step 2: Convert to fraction form
    30,496/65,984 = 65,984/x
  3. Step 3: Cross multiply
    30,496x = 65,984 × 65,984
  4. Step 4: Simplify right side
    30,496x = 4,353,888,256
  5. Step 5: Solve for x
    x = 4,353,888,256/30,496
  6. Step 6: Final answer
    x = 142,769.16

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.