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Finding the Fourth Proportional to 1,408.34, 2,109.32 and 678.44

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Solution

The fourth proportional to 1,408.34, 2,109.32 and 678.44 is: 1,016.12

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,408.34 : 2,109.32 = 678.44 : x
  2. Step 2: Convert to fraction form
    1,408.34/2,109.32 = 678.44/x
  3. Step 3: Cross multiply
    1,408.34x = 2,109.32 × 678.44
  4. Step 4: Simplify right side
    1,408.34x = 1,431,047.06
  5. Step 5: Solve for x
    x = 1,431,047.06/1,408.34
  6. Step 6: Final answer
    x = 1,016.12

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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.