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Finding the Fourth Proportional to 1,689.28, 2,534.16 and 823

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Solution

The fourth proportional to 1,689.28, 2,534.16 and 823 is: 1,234.62

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,689.28 : 2,534.16 = 823 : x
  2. Step 2: Convert to fraction form
    1,689.28/2,534.16 = 823/x
  3. Step 3: Cross multiply
    1,689.28x = 2,534.16 × 823
  4. Step 4: Simplify right side
    1,689.28x = 2,085,613.68
  5. Step 5: Solve for x
    x = 2,085,613.68/1,689.28
  6. Step 6: Final answer
    x = 1,234.62

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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.