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Finding the Third Proportional to 32,084 and 78,023

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Solution

The third proportional to 32,084 and 78,023 is: 189,739.08

Step by Step Solution

  1. Step 1: Write the proportion equation
    32,084 : 78,023 = 78,023 : x
  2. Step 2: Convert to fraction form
    32,084/78,023 = 78,023/x
  3. Step 3: Cross multiply
    32,084x = 78,023 × 78,023
  4. Step 4: Simplify right side
    32,084x = 6,087,588,529
  5. Step 5: Solve for x
    x = 6,087,588,529/32,084
  6. Step 6: Final answer
    x = 189,739.08

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Why These Related Problems?

These problems maintain the same ratio (2.43) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.