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Finding the Fourth Proportional to 1,406.73, 2,109.57 and 419.22

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Solution

The fourth proportional to 1,406.73, 2,109.57 and 419.22 is: 628.67

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,406.73 : 2,109.57 = 419.22 : x
  2. Step 2: Convert to fraction form
    1,406.73/2,109.57 = 419.22/x
  3. Step 3: Cross multiply
    1,406.73x = 2,109.57 × 419.22
  4. Step 4: Simplify right side
    1,406.73x = 884,373.94
  5. Step 5: Solve for x
    x = 884,373.94/1,406.73
  6. Step 6: Final answer
    x = 628.67

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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.