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Finding the Fourth Proportional to 1,406.51, 2,109.76 and 419.33

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Solution

The fourth proportional to 1,406.51, 2,109.76 and 419.33 is: 628.99

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,406.51 : 2,109.76 = 419.33 : x
  2. Step 2: Convert to fraction form
    1,406.51/2,109.76 = 419.33/x
  3. Step 3: Cross multiply
    1,406.51x = 2,109.76 × 419.33
  4. Step 4: Simplify right side
    1,406.51x = 884,683.56
  5. Step 5: Solve for x
    x = 884,683.56/1,406.51
  6. Step 6: Final answer
    x = 628.99

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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.