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Finding the Third Proportional to 822 and 2,178

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Solution

The third proportional to 822 and 2,178 is: 5,770.91

Step by Step Solution

  1. Step 1: Write the proportion equation
    822 : 2,178 = 2,178 : x
  2. Step 2: Convert to fraction form
    822/2,178 = 2,178/x
  3. Step 3: Cross multiply
    822x = 2,178 × 2,178
  4. Step 4: Simplify right side
    822x = 4,743,684
  5. Step 5: Solve for x
    x = 4,743,684/822
  6. Step 6: Final answer
    x = 5,770.91

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Why These Related Problems?

These problems maintain the same ratio (2.65) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.