Question

2(a) Solve: [7(x+4)-2/3(x-6)] ≤ 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?

Accepted Answer

(a) 7(x+4) - 2(x-6)/3 ≤ 2[x-3(x+5)]
Multiply through by 3 to clear the fraction:
21(x+4) - 2(x-6) ≤ 6(x-3x-15)
21x+84-2x+12 ≤ 6(-2x-15)
19x+96 ≤ -12x-90
19x+12x ≤ -90-96
31x ≤ -186
x ≤ -6

(b) Let x = number of tricycles and y = number of taxicabs.
x+y=20 ......(i)
2x+4y=66 ......(ii)
From (i): y=20-x. Substitute into (ii): 2x+4(20-x)=66 → 2x+80-4x=66 → -2x=-14 → x=7
The company has 7 tricycles.

WAEC Mathematics 2016 Theory — Question 2

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