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Finding the Fourth Proportional to 456, 684 and 199.50

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Solution

The fourth proportional to 456, 684 and 199.50 is: 299.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    456 : 684 = 199.50 : x
  2. Step 2: Convert to fraction form
    456/684 = 199.50/x
  3. Step 3: Cross multiply
    456x = 684 × 199.50
  4. Step 4: Simplify right side
    456x = 136,458
  5. Step 5: Solve for x
    x = 136,458/456
  6. Step 6: Final answer
    x = 299.25

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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.