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Finding the Fourth Proportional to 1,106.34, 1,657.89 and 782.34

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Solution

The fourth proportional to 1,106.34, 1,657.89 and 782.34 is: 1,172.36

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,106.34 : 1,657.89 = 782.34 : x
  2. Step 2: Convert to fraction form
    1,106.34/1,657.89 = 782.34/x
  3. Step 3: Cross multiply
    1,106.34x = 1,657.89 × 782.34
  4. Step 4: Simplify right side
    1,106.34x = 1,297,033.66
  5. Step 5: Solve for x
    x = 1,297,033.66/1,106.34
  6. Step 6: Final answer
    x = 1,172.36

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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.