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Finding the Third Proportional to 274.13 and 419.63

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Solution

The third proportional to 274.13 and 419.63 is: 642.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    274.13 : 419.63 = 419.63 : x
  2. Step 2: Convert to fraction form
    274.13/419.63 = 419.63/x
  3. Step 3: Cross multiply
    274.13x = 419.63 × 419.63
  4. Step 4: Simplify right side
    274.13x = 176,085.14
  5. Step 5: Solve for x
    x = 176,085.14/274.13
  6. Step 6: Final answer
    x = 642.35

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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.