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Finding the Third Proportional to 416.50 and 964.20

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Solution

The third proportional to 416.50 and 964.20 is: 2,232.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    416.50 : 964.20 = 964.20 : x
  2. Step 2: Convert to fraction form
    416.50/964.20 = 964.20/x
  3. Step 3: Cross multiply
    416.50x = 964.20 × 964.20
  4. Step 4: Simplify right side
    416.50x = 929,672.60
  5. Step 5: Solve for x
    x = 929,672.60/416.50
  6. Step 6: Final answer
    x = 2,232.13

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Why These Related Problems?

These problems maintain the same ratio (2.32) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.