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Finding the Fourth Proportional to 809.65, 1,214.41 and 419.23

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Solution

The fourth proportional to 809.65, 1,214.41 and 419.23 is: 628.81

Step by Step Solution

  1. Step 1: Write the proportion equation
    809.65 : 1,214.41 = 419.23 : x
  2. Step 2: Convert to fraction form
    809.65/1,214.41 = 419.23/x
  3. Step 3: Cross multiply
    809.65x = 1,214.41 × 419.23
  4. Step 4: Simplify right side
    809.65x = 509,117.10
  5. Step 5: Solve for x
    x = 509,117.10/809.65
  6. Step 6: Final answer
    x = 628.81

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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.