Theory question 102
Inequalities(a) Solve: 7(x + 4) − ⅔(x − 6) ≤ 2[x − 3(x + 5)].
(b) A transport company has a total 20 vehicles made up of tricycles and taxicabs. Each tricycle carries 2 passengers while each taxicab carries 4 passengers. If the 20 vehicles carry a total of 66 passengers at a time, how many tricycles does the company have?
Show the model answer
Model answer
(a) 7x + 28 − ⅔x + 4 ≤ 2(−2x − 15) = −4x − 30
7x − ⅔x + 4x ≤ −62 → (31/3)x ≤ −62 → x ≤ −6
(b) Let t = tricycles, c = taxicabs: t + c = 20 and 2t + 4c = 66
2t + 4(20 − t) = 66 → 80 − 2t = 66 → t = 7
The company has 7 tricycles (and 13 taxicabs).
Explanation
Remove the inner bracket first in (a).