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Finding the Fourth Proportional to 1,006.53, 1,509.86 and 313.26

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Solution

The fourth proportional to 1,006.53, 1,509.86 and 313.26 is: 469.91

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,006.53 : 1,509.86 = 313.26 : x
  2. Step 2: Convert to fraction form
    1,006.53/1,509.86 = 313.26/x
  3. Step 3: Cross multiply
    1,006.53x = 1,509.86 × 313.26
  4. Step 4: Simplify right side
    1,006.53x = 472,978.74
  5. Step 5: Solve for x
    x = 472,978.74/1,006.53
  6. Step 6: Final answer
    x = 469.91

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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.