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Finding the Fourth Proportional to 1,105.90, 1,659.03 and 412.75

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Solution

The fourth proportional to 1,105.90, 1,659.03 and 412.75 is: 619.19

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,105.90 : 1,659.03 = 412.75 : x
  2. Step 2: Convert to fraction form
    1,105.90/1,659.03 = 412.75/x
  3. Step 3: Cross multiply
    1,105.90x = 1,659.03 × 412.75
  4. Step 4: Simplify right side
    1,105.90x = 684,764.63
  5. Step 5: Solve for x
    x = 684,764.63/1,105.90
  6. Step 6: Final answer
    x = 619.19

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.