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Finding the Third Proportional to 274.50 and 419.81

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Solution

The third proportional to 274.50 and 419.81 is: 642.05

Step by Step Solution

  1. Step 1: Write the proportion equation
    274.50 : 419.81 = 419.81 : x
  2. Step 2: Convert to fraction form
    274.50/419.81 = 419.81/x
  3. Step 3: Cross multiply
    274.50x = 419.81 × 419.81
  4. Step 4: Simplify right side
    274.50x = 176,242.54
  5. Step 5: Solve for x
    x = 176,242.54/274.50
  6. Step 6: Final answer
    x = 642.05

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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.