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Finding the Third Proportional to 37,965 and 83,085

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Solution

The third proportional to 37,965 and 83,085 is: 181,828.45

Step by Step Solution

  1. Step 1: Write the proportion equation
    37,965 : 83,085 = 83,085 : x
  2. Step 2: Convert to fraction form
    37,965/83,085 = 83,085/x
  3. Step 3: Cross multiply
    37,965x = 83,085 × 83,085
  4. Step 4: Simplify right side
    37,965x = 6,903,117,225
  5. Step 5: Solve for x
    x = 6,903,117,225/37,965
  6. Step 6: Final answer
    x = 181,828.45

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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.