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Finding the Fourth Proportional to 1,006.21, 1,509.47 and 312.80

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Solution

The fourth proportional to 1,006.21, 1,509.47 and 312.80 is: 469.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,006.21 : 1,509.47 = 312.80 : x
  2. Step 2: Convert to fraction form
    1,006.21/1,509.47 = 312.80/x
  3. Step 3: Cross multiply
    1,006.21x = 1,509.47 × 312.80
  4. Step 4: Simplify right side
    1,006.21x = 472,162.22
  5. Step 5: Solve for x
    x = 472,162.22/1,006.21
  6. Step 6: Final answer
    x = 469.25

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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.