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Finding the Fourth Proportional to 1,023.14, 1,409.44 and 813.24

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Solution

The fourth proportional to 1,023.14, 1,409.44 and 813.24 is: 1,120.29

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,023.14 : 1,409.44 = 813.24 : x
  2. Step 2: Convert to fraction form
    1,023.14/1,409.44 = 813.24/x
  3. Step 3: Cross multiply
    1,023.14x = 1,409.44 × 813.24
  4. Step 4: Simplify right side
    1,023.14x = 1,146,212.99
  5. Step 5: Solve for x
    x = 1,146,212.99/1,023.14
  6. Step 6: Final answer
    x = 1,120.29

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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.