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Finding the Fourth Proportional to 1,106.16, 1,659.34 and 412.80

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Solution

The fourth proportional to 1,106.16, 1,659.34 and 412.80 is: 619.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,106.16 : 1,659.34 = 412.80 : x
  2. Step 2: Convert to fraction form
    1,106.16/1,659.34 = 412.80/x
  3. Step 3: Cross multiply
    1,106.16x = 1,659.34 × 412.80
  4. Step 4: Simplify right side
    1,106.16x = 684,975.55
  5. Step 5: Solve for x
    x = 684,975.55/1,106.16
  6. Step 6: Final answer
    x = 619.24

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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.