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Finding the Fourth Proportional to 1,005.14, 1,507.22 and 419.97

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Solution

The fourth proportional to 1,005.14, 1,507.22 and 419.97 is: 629.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,005.14 : 1,507.22 = 419.97 : x
  2. Step 2: Convert to fraction form
    1,005.14/1,507.22 = 419.97/x
  3. Step 3: Cross multiply
    1,005.14x = 1,507.22 × 419.97
  4. Step 4: Simplify right side
    1,005.14x = 632,984.42
  5. Step 5: Solve for x
    x = 632,984.42/1,005.14
  6. Step 6: Final answer
    x = 629.75

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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.