NECO Mathematics 2007 Theory — Question 2
Question 2 of 50 from the National Examinations Council (NECO) Mathematics 2007 Theory paper, with the correct answer and a full explanation.
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2. (a) A factory has 80 employees. If the number of men doubled and the women tripled, the staff strength would be 190. Find the initial number of men and women working at the factory. (b) Solve for x if 25^(3x+2)=5^(2x-1). (8 marks)
Model answer
(a) Let m = men, w = women. m+w=80 ... (i). 2m+3w=190 ... (ii). From (i), m=80-w. Substituting into (ii): 2(80-w)+3w=190, 160-2w+3w=190, w=30. So m=50. Initial: 50 men, 30 women. (b) 25^(3x+2) = (5^2)^(3x+2) = 5^(6x+4). Setting equal to 5^(2x-1): 6x+4=2x-1, 4x=-5, x=-5/4.
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