In the Department of Mathematical and Computational Science, 83% of lecture hall
ID: 3042468 • Letter: I
Question
In the Department of Mathematical and Computational Science, 83% of lecture halls have chalkboards, and the other 17% have dry-erase boards. Of the classes taught in rooms with chalkboards, 75% are mathematics courses, 15% are computer science courses, and 10% are statistics courses. Of the classes taught in rooms with dry-erase boards, 65% are computer science courses, 8% are mathematics courses, and 27% are statistics courses. What percent of courses at the college are mathematics or statistics?
Explanation / Answer
Let the total number of lecture halls = x
No of halls with chalkboards = 83% = 0.83x and number of halls with dry erase boards = 0.17x
Mathematics in rooms with chalkboards = 75% of 0.83x = 0.75 * 0.83x = 0.6225x
Mathematics in rooms with dry erase boards = 8% of 0.17x = 0.08 * 0.83x = 0.0136x
Total number of math classes = 0.6225x + 0.0136x = 0.6361x
Statistics in rooms with chalkboards = 10% of 0.83x = 0.1 * 0.17x = 0.083x
Statistics in rooms with dry erase boards = 27% of 0.17x = 0.27 * 0.17x = 0.0459x
Total number of Statistic classes = 0.083x + 0.0459x = 0.1289x
Total maths and Statistics = 0.6361 + 0.1289x = 0.765x
Therefore % of courses which are statistics or Mathematics = (0.765x/x) * 100 = 76.5%