Question

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)

Accepted 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.

GCE Mathematics 2025 Theory — Question 2

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