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Finding the Fourth Proportional to 1,020.66, 1,409.31 and 784.24

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Solution

The fourth proportional to 1,020.66, 1,409.31 and 784.24 is: 1,082.86

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,020.66 : 1,409.31 = 784.24 : x
  2. Step 2: Convert to fraction form
    1,020.66/1,409.31 = 784.24/x
  3. Step 3: Cross multiply
    1,020.66x = 1,409.31 × 784.24
  4. Step 4: Simplify right side
    1,020.66x = 1,105,231.79
  5. Step 5: Solve for x
    x = 1,105,231.79/1,020.66
  6. Step 6: Final answer
    x = 1,082.86

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Why These Related Problems?

These problems maintain the same ratio (1.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.