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Finding the Fourth Proportional to 1,026.36, 1,538.91 and 409.95

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Solution

The fourth proportional to 1,026.36, 1,538.91 and 409.95 is: 614.67

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,026.36 : 1,538.91 = 409.95 : x
  2. Step 2: Convert to fraction form
    1,026.36/1,538.91 = 409.95/x
  3. Step 3: Cross multiply
    1,026.36x = 1,538.91 × 409.95
  4. Step 4: Simplify right side
    1,026.36x = 630,876.15
  5. Step 5: Solve for x
    x = 630,876.15/1,026.36
  6. Step 6: Final answer
    x = 614.67

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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.