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Finding the Fourth Proportional to 1,406.70, 2,109.65 and 419.48

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Solution

The fourth proportional to 1,406.70, 2,109.65 and 419.48 is: 629.09

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,406.70 : 2,109.65 = 419.48 : x
  2. Step 2: Convert to fraction form
    1,406.70/2,109.65 = 419.48/x
  3. Step 3: Cross multiply
    1,406.70x = 2,109.65 × 419.48
  4. Step 4: Simplify right side
    1,406.70x = 884,944.91
  5. Step 5: Solve for x
    x = 884,944.91/1,406.70
  6. Step 6: Final answer
    x = 629.09

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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.