The following problem "Example 2" provides solution, however I need to solve this problem in a better and faster way instead of provided solution as shown below. Please help.

Example 2 In a survey, 113 business executives were asked if they regularly read the Wall Street Journal, Business Week magazine, and Time magazine. The results of the survey are as follows: 88 read the Journal. 76 read Business Week. 6 read only the Journal. 85 read Time. 5 read only Business Week. 8 read only Time. 42 read all three. How many read none of the three publications? Solution Letting J, B, and T represent the sets of Journal, Business Week, and Time readers, we draw a Venn diagram and place the numbers given above in the diagram, as shown at the right. (Be sure you understand the placement of each number in the U B diagram.) To find the numbers for the remaining regions of the dia- 88 gram, we let a represent the num- 42 ber of executives who read just the Journal and Business Week, b represent the number who read just Business Week and Time, and c represent the number who read T just the Journal and Time. We can X then write the following system of 2 113 equations: 88 = 6+42 +a+ c, or 40 = a+ c 76 = 5+42+atb, 29 = a + b 85 = 8+42+b+ c, 35 = b+ c Solving this system gives a = 17, b = 12, and c = 23. The number x, representing those who read none of the three publications, can be found by adding the numbers within the three circles and subtracting the sum from 113. This gives x = 0, which means that every one of the business executives surveyed reads at least one of the three publications