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Finding the Fourth Proportional to 296.38, 409 and 165.40

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Solution

The fourth proportional to 296.38, 409 and 165.40 is: 228.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    296.38 : 409 = 165.40 : x
  2. Step 2: Convert to fraction form
    296.38/409 = 165.40/x
  3. Step 3: Cross multiply
    296.38x = 409 × 165.40
  4. Step 4: Simplify right side
    296.38x = 67,648.60
  5. Step 5: Solve for x
    x = 67,648.60/296.38
  6. Step 6: Final answer
    x = 228.25

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Why These Related Problems?

These problems maintain the same ratio (1.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.