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Finding the Third Proportional to 463 and 972

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Solution

The third proportional to 463 and 972 is: 2,040.57

Step by Step Solution

  1. Step 1: Write the proportion equation
    463 : 972 = 972 : x
  2. Step 2: Convert to fraction form
    463/972 = 972/x
  3. Step 3: Cross multiply
    463x = 972 × 972
  4. Step 4: Simplify right side
    463x = 944,784
  5. Step 5: Solve for x
    x = 944,784/463
  6. Step 6: Final answer
    x = 2,040.57

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Why These Related Problems?

These problems maintain the same ratio (2.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.