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Finding the Fourth Proportional to 685.94, 1,029.33 and 412.10

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Solution

The fourth proportional to 685.94, 1,029.33 and 412.10 is: 618.40

Step by Step Solution

  1. Step 1: Write the proportion equation
    685.94 : 1,029.33 = 412.10 : x
  2. Step 2: Convert to fraction form
    685.94/1,029.33 = 412.10/x
  3. Step 3: Cross multiply
    685.94x = 1,029.33 × 412.10
  4. Step 4: Simplify right side
    685.94x = 424,186.89
  5. Step 5: Solve for x
    x = 424,186.89/685.94
  6. Step 6: Final answer
    x = 618.40

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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.