Theory question 106
Linear and Simultaneous Equations(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 ⅓ 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, 13/30 by air and 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 (A) were interviewed; (B) travelled by air only?
Show the model answer
(a) (M − 15)/2 = M/3 → 3M − 45 = 2M → M = 45.
(b)(i) Two overlapping circles, Road and Air: road only 2/3 − 4/15 = 2/5, both 4/15, air only 13/30 − 4/15 = 1/6, outside 20 tourists.
(ii)(A) Road or air = 2/5 + 4/15 + 1/6 = 5/6, so neither = 1/6 of the total = 20. Total = 120.
(B) Air only = 1/6 × 120 = 20.
Write each region as a fraction of the total, then use the 20 who used neither.