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Finding the Fourth Proportional to 1,023.70, 1,409.12 and 728.50

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Solution

The fourth proportional to 1,023.70, 1,409.12 and 728.50 is: 1,002.78

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,023.70 : 1,409.12 = 728.50 : x
  2. Step 2: Convert to fraction form
    1,023.70/1,409.12 = 728.50/x
  3. Step 3: Cross multiply
    1,023.70x = 1,409.12 × 728.50
  4. Step 4: Simplify right side
    1,023.70x = 1,026,543.92
  5. Step 5: Solve for x
    x = 1,026,543.92/1,023.70
  6. Step 6: Final answer
    x = 1,002.78

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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.