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Finding the Third Proportional to 419.50 and 640.25

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Solution

The third proportional to 419.50 and 640.25 is: 977.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    419.50 : 640.25 = 640.25 : x
  2. Step 2: Convert to fraction form
    419.50/640.25 = 640.25/x
  3. Step 3: Cross multiply
    419.50x = 640.25 × 640.25
  4. Step 4: Simplify right side
    419.50x = 409,920.06
  5. Step 5: Solve for x
    x = 409,920.06/419.50
  6. Step 6: Final answer
    x = 977.16

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Why These Related Problems?

These problems maintain the same ratio (1.53) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.