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Finding the Fourth Proportional to 1,023.85, 1,538.07 and 971.47

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Solution

The fourth proportional to 1,023.85, 1,538.07 and 971.47 is: 1,459.38

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,023.85 : 1,538.07 = 971.47 : x
  2. Step 2: Convert to fraction form
    1,023.85/1,538.07 = 971.47/x
  3. Step 3: Cross multiply
    1,023.85x = 1,538.07 × 971.47
  4. Step 4: Simplify right side
    1,023.85x = 1,494,188.86
  5. Step 5: Solve for x
    x = 1,494,188.86/1,023.85
  6. Step 6: Final answer
    x = 1,459.38

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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.