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Finding the Third Proportional to 7,822 and 17,024

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Solution

The third proportional to 7,822 and 17,024 is: 37,051.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,822 : 17,024 = 17,024 : x
  2. Step 2: Convert to fraction form
    7,822/17,024 = 17,024/x
  3. Step 3: Cross multiply
    7,822x = 17,024 × 17,024
  4. Step 4: Simplify right side
    7,822x = 289,816,576
  5. Step 5: Solve for x
    x = 289,816,576/7,822
  6. Step 6: Final answer
    x = 37,051.47

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.