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Finding the Fourth Proportional to 1,109.64, 1,663.37 and 416.13

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Solution

The fourth proportional to 1,109.64, 1,663.37 and 416.13 is: 623.78

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,109.64 : 1,663.37 = 416.13 : x
  2. Step 2: Convert to fraction form
    1,109.64/1,663.37 = 416.13/x
  3. Step 3: Cross multiply
    1,109.64x = 1,663.37 × 416.13
  4. Step 4: Simplify right side
    1,109.64x = 692,167.76
  5. Step 5: Solve for x
    x = 692,167.76/1,109.64
  6. Step 6: Final answer
    x = 623.78

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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.