(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?
(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.
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