(a) A boy had M Dalasis (D). He spent D15 and shared the remainder equally with his sister. If the sister’s share was equal to (frac{1}{3}) of M, find the value of M.
(b) A number of tourists were interviewed on their choice of means of travel. Two- thirds said that they travelled by road, (frac{13}{30}) by air and (frac{4}{15}) by both air and road. If 20 tourists did not travel by either air or road ; (i) represent the information on a Venn diagram ; (ii) how many tourists (1) were interviewed ; (2) travelled by air only?
Explanation
(a) Amount shared = D(M – 15)
Sister’s share = (frac{D(M – 15)}{2})
(implies frac{D(M – 15)}{2} = frac{1}{3}M)
(2M = 3(M – 15) implies 3M – 2M = 45)
(M = 45.00)
(b) (i)
(ii) (1) Total no interviewed = (frac{2}{5}x + frac{4}{15}x + frac{1}{6}x + 20 = x)
(therefore 12x + 8x + 5x + 600 = 30x) (Multiplying through with their LCM which is 30)
(600 = 30x – 12x – 8x – 5x = 5x implies 600 = 5x)
(x = frac{600}{5} = 120)
(2) Those that travelled by air only = ((frac{13}{30} times 120) – (frac{4}{15} times 120))
= (52 – 32 = 20)