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Finding the Fourth Proportional to 1,106.61, 1,659.93 and 457.21

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Solution

The fourth proportional to 1,106.61, 1,659.93 and 457.21 is: 685.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,106.61 : 1,659.93 = 457.21 : x
  2. Step 2: Convert to fraction form
    1,106.61/1,659.93 = 457.21/x
  3. Step 3: Cross multiply
    1,106.61x = 1,659.93 × 457.21
  4. Step 4: Simplify right side
    1,106.61x = 758,936.60
  5. Step 5: Solve for x
    x = 758,936.60/1,106.61
  6. Step 6: Final answer
    x = 685.82

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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.