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Finding the Fourth Proportional to 1,109.84, 1,663.86 and 416.12

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Solution

The fourth proportional to 1,109.84, 1,663.86 and 416.12 is: 623.84

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,109.84 : 1,663.86 = 416.12 : x
  2. Step 2: Convert to fraction form
    1,109.84/1,663.86 = 416.12/x
  3. Step 3: Cross multiply
    1,109.84x = 1,663.86 × 416.12
  4. Step 4: Simplify right side
    1,109.84x = 692,365.42
  5. Step 5: Solve for x
    x = 692,365.42/1,109.84
  6. Step 6: Final answer
    x = 623.84

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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.