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Finding the Fourth Proportional to 1,106.02, 1,659.30 and 782.02

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Solution

The fourth proportional to 1,106.02, 1,659.30 and 782.02 is: 1,173.22

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,106.02 : 1,659.30 = 782.02 : x
  2. Step 2: Convert to fraction form
    1,106.02/1,659.30 = 782.02/x
  3. Step 3: Cross multiply
    1,106.02x = 1,659.30 × 782.02
  4. Step 4: Simplify right side
    1,106.02x = 1,297,605.79
  5. Step 5: Solve for x
    x = 1,297,605.79/1,106.02
  6. Step 6: Final answer
    x = 1,173.22

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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.