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Finding the Fourth Proportional to 741.82, 1,023.72 and 410.24

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Solution

The fourth proportional to 741.82, 1,023.72 and 410.24 is: 566.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    741.82 : 1,023.72 = 410.24 : x
  2. Step 2: Convert to fraction form
    741.82/1,023.72 = 410.24/x
  3. Step 3: Cross multiply
    741.82x = 1,023.72 × 410.24
  4. Step 4: Simplify right side
    741.82x = 419,970.89
  5. Step 5: Solve for x
    x = 419,970.89/741.82
  6. Step 6: Final answer
    x = 566.14

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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.