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Finding the Fourth Proportional to 106.65, 159.75 and 77.67

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Solution

The fourth proportional to 106.65, 159.75 and 77.67 is: 116.34

Step by Step Solution

  1. Step 1: Write the proportion equation
    106.65 : 159.75 = 77.67 : x
  2. Step 2: Convert to fraction form
    106.65/159.75 = 77.67/x
  3. Step 3: Cross multiply
    106.65x = 159.75 × 77.67
  4. Step 4: Simplify right side
    106.65x = 12,407.78
  5. Step 5: Solve for x
    x = 12,407.78/106.65
  6. Step 6: Final answer
    x = 116.34

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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.