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Finding the Fourth Proportional to 1,026.32, 1,538.76 and 409.84

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Solution

The fourth proportional to 1,026.32, 1,538.76 and 409.84 is: 614.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,026.32 : 1,538.76 = 409.84 : x
  2. Step 2: Convert to fraction form
    1,026.32/1,538.76 = 409.84/x
  3. Step 3: Cross multiply
    1,026.32x = 1,538.76 × 409.84
  4. Step 4: Simplify right side
    1,026.32x = 630,645.40
  5. Step 5: Solve for x
    x = 630,645.40/1,026.32
  6. Step 6: Final answer
    x = 614.47

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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.