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Finding the Fourth Proportional to 1,315.40, 1,971.04 and 827.42

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Solution

The fourth proportional to 1,315.40, 1,971.04 and 827.42 is: 1,239.83

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,315.40 : 1,971.04 = 827.42 : x
  2. Step 2: Convert to fraction form
    1,315.40/1,971.04 = 827.42/x
  3. Step 3: Cross multiply
    1,315.40x = 1,971.04 × 827.42
  4. Step 4: Simplify right side
    1,315.40x = 1,630,877.92
  5. Step 5: Solve for x
    x = 1,630,877.92/1,315.40
  6. Step 6: Final answer
    x = 1,239.83

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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.