(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 = \((\frac{13}{30} \times 120) - (\frac{4}{15} \times 120)\)
= \(52 - 32 = 20\)