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Finding the Fourth Proportional to 1,077.84, 1,616.40 and 419.67

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Solution

The fourth proportional to 1,077.84, 1,616.40 and 419.67 is: 629.36

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,077.84 : 1,616.40 = 419.67 : x
  2. Step 2: Convert to fraction form
    1,077.84/1,616.40 = 419.67/x
  3. Step 3: Cross multiply
    1,077.84x = 1,616.40 × 419.67
  4. Step 4: Simplify right side
    1,077.84x = 678,346.95
  5. Step 5: Solve for x
    x = 678,346.95/1,077.84
  6. Step 6: Final answer
    x = 629.36

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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.