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Finding the Third Proportional to 32,984 and 77,822

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Solution

The third proportional to 32,984 and 77,822 is: 183,612.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    32,984 : 77,822 = 77,822 : x
  2. Step 2: Convert to fraction form
    32,984/77,822 = 77,822/x
  3. Step 3: Cross multiply
    32,984x = 77,822 × 77,822
  4. Step 4: Simplify right side
    32,984x = 6,056,263,684
  5. Step 5: Solve for x
    x = 6,056,263,684/32,984
  6. Step 6: Final answer
    x = 183,612.17

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Why These Related Problems?

These problems maintain the same ratio (2.36) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.