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Finding the Fourth Proportional to 1,053.72, 1,578.42 and 822.36

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Solution

The fourth proportional to 1,053.72, 1,578.42 and 822.36 is: 1,231.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,053.72 : 1,578.42 = 822.36 : x
  2. Step 2: Convert to fraction form
    1,053.72/1,578.42 = 822.36/x
  3. Step 3: Cross multiply
    1,053.72x = 1,578.42 × 822.36
  4. Step 4: Simplify right side
    1,053.72x = 1,298,029.47
  5. Step 5: Solve for x
    x = 1,298,029.47/1,053.72
  6. Step 6: Final answer
    x = 1,231.85

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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.