(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...
Question 1 Report
(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?
Answer Details
(a) Solve \(7(x+4)-\tfrac{2}{3}(x-6)\le 2[x-3(x+5)]\).
Right side: \(x-3(x+5)=x-3x-15=-2x-15\), so \(2(-2x-15)=-4x-30\).
Left side: \(7x+28-\tfrac{2}{3}(x-6)=7x+28-\tfrac{2}{3}x+4=\tfrac{19}{3}x+32\).
Inequality: \(\tfrac{19}{3}x+32\le -4x-30\). Multiply through by 3:
\[19x+96\le -12x-90\Rightarrow 31x\le -186\Rightarrow x\le -6\]\(x\le -6\)
(b) Let \(t\) = tricycles and \(c\) = taxicabs.
Vehicles: \(t+c=20\).
Passengers: \(2t+4c=66\).
From the first, \(c=20-t\). Substitute:
\[2t+4(20-t)=66\Rightarrow 2t+80-4t=66\Rightarrow -2t=-14\Rightarrow t=7\]The company has 7 tricycles (and 13 taxicabs).
Download The App On Google Playstore
Everything you need to excel in your exams
