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Finding the Third Proportional to 974 and 1,462

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Solution

The third proportional to 974 and 1,462 is: 2,194.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    974 : 1,462 = 1,462 : x
  2. Step 2: Convert to fraction form
    974/1,462 = 1,462/x
  3. Step 3: Cross multiply
    974x = 1,462 × 1,462
  4. Step 4: Simplify right side
    974x = 2,137,444
  5. Step 5: Solve for x
    x = 2,137,444/974
  6. Step 6: Final answer
    x = 2,194.50

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.