Theory question 106
Sets(a) In a class of 80 students, ¾ study Biology and ⅗ study Physics. If each student studies at least one of the subjects: (i) draw a venn diagram to represent this information; (ii) how many students study both subjects; (iii) find the fraction of the class that study Biology but not Physics.
(b) Johnson and Jocatol Ltd. owned a business office with floor measuring 15 m by 8 m which was to be carpeted. The cost of carpeting was GH¢ 890.00 per square metre. If a total of GH¢ 216,120.00 was spent on painting and carpeting, how much was the cost of painting?
Show the model answer
(a) n(B) = 60, n(P) = 48, n(U) = 80
(i) Two overlapping circles B and P with regions 60 − x, x, 48 − x and nothing outside
(ii) 60 − x + x + 48 − x = 80 → x = 28
(iii) Biology only = 60 − 28 = 32; fraction = 32/80 = 2/5
(b) Floor area = 15 × 8 = 120 m2; carpeting = 120 × 890 = GH¢106,800
Painting = 216,120 − 106,800 = GH¢109,320
Every student is in at least one circle, so nothing goes outside the circles.