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Finding the Fourth Proportional to 698.10, 1,048.26 and 409.74

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Solution

The fourth proportional to 698.10, 1,048.26 and 409.74 is: 615.26

Step by Step Solution

  1. Step 1: Write the proportion equation
    698.10 : 1,048.26 = 409.74 : x
  2. Step 2: Convert to fraction form
    698.10/1,048.26 = 409.74/x
  3. Step 3: Cross multiply
    698.10x = 1,048.26 × 409.74
  4. Step 4: Simplify right side
    698.10x = 429,514.05
  5. Step 5: Solve for x
    x = 429,514.05/698.10
  6. Step 6: Final answer
    x = 615.26

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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.