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Finding the Fourth Proportional to 822, 1,231.46 and 410.66

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Solution

The fourth proportional to 822, 1,231.46 and 410.66 is: 615.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    822 : 1,231.46 = 410.66 : x
  2. Step 2: Convert to fraction form
    822/1,231.46 = 410.66/x
  3. Step 3: Cross multiply
    822x = 1,231.46 × 410.66
  4. Step 4: Simplify right side
    822x = 505,703.15
  5. Step 5: Solve for x
    x = 505,703.15/822
  6. Step 6: Final answer
    x = 615.21

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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.