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Finding the Fourth Proportional to 1,006.29, 1,509.65 and 312.94

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Solution

The fourth proportional to 1,006.29, 1,509.65 and 312.94 is: 469.48

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,006.29 : 1,509.65 = 312.94 : x
  2. Step 2: Convert to fraction form
    1,006.29/1,509.65 = 312.94/x
  3. Step 3: Cross multiply
    1,006.29x = 1,509.65 × 312.94
  4. Step 4: Simplify right side
    1,006.29x = 472,433.65
  5. Step 5: Solve for x
    x = 472,433.65/1,006.29
  6. Step 6: Final answer
    x = 469.48

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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.