(a) Solve : (7(x + 4) – frac{2}{3}(x – 6) leq 2[x – 3(x + 5)])
(b) A transport company has a total of 20 vehicles made up of tricycle and taxicabs. Each tricycle carries 2 passengers while each taxicab carries four passengers. If the 20 vehicles carry a total of 66 passengers at a time, how many tricycles does the company have?
Explanation
(a) (7(x + 4) – frac{2}{3}(x – 6) leq 2[x – 3(x + 5)])
Multiply through by 3 to clear the fraction :
(21(x + 4) – 2(x – 6) leq 6[x – 3(x + 5)])
(21x + 84 – 2x + 12 leq 6x – 18x – 90)
(19x + 96 leq -12x – 90)
(19x + 12x leq -90 – 96)
(31x leq – 186)
Hence, (x leq -6).
(b) Let : t represent number of tricycles; and b represent number of taxicabs
Then (t + b = 20 … (1))
(2t + 4b = 66 …. (2))
From (1), b = 20 – t. Put that into eqtn (2), we have:
(2t + 4(20 – t) = 2t + 80 – 4t = 66)
(80 – 66 = 14 = 2t )
(t = 7)
The transport company has 7 tricycles.