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Finding the Third Proportional to 589.50 and 1,463.63

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Solution

The third proportional to 589.50 and 1,463.63 is: 3,633.92

Step by Step Solution

  1. Step 1: Write the proportion equation
    589.50 : 1,463.63 = 1,463.63 : x
  2. Step 2: Convert to fraction form
    589.50/1,463.63 = 1,463.63/x
  3. Step 3: Cross multiply
    589.50x = 1,463.63 × 1,463.63
  4. Step 4: Simplify right side
    589.50x = 2,142,198.14
  5. Step 5: Solve for x
    x = 2,142,198.14/589.50
  6. Step 6: Final answer
    x = 3,633.92

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Why These Related Problems?

These problems maintain the same ratio (2.48) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.