(a) Find the smallest integer that satisfies the inequality \(x + 8 < 4x - 15\). (b) A sales girl is paid a monthly salary of N2,500 in addition to a commission of 5 kobo in the naira on all sales made by her during the month. If her sales for a month amounts to N200,000.00, calculate her income for that month. (c) The diagram shows a window consisting of a rectangular and semi- circular parts. The radius of the semi- circular part is 35 cm and the height of the rectangular part is 50 cm. Find the area of the window. [Take \(\pi = \frac{22}{7}\)].
Explanation
(a) \(x + 8 < 4x - 15 \implies 4x - 15 > x + 8\) \(4x - x > 8 + 15 \implies 3x > 23\) \(x > \frac{23}{3}\) \(x > 7\frac{2}{3}\). (b) Extra income = 5k of N200,000 = \(\frac{5}{100} \times N200,000\) = \(N10,000\) Total income = Monthly income + commission = N(2,500 + 10,000) = N12,500. (c) Area of semi- circle = \(\frac{\pi r^{2}}{2}\) = \(\frac{1}{2} \times \frac{22}{7} \times 35 \times 35\) = \(1925 cm^{2}\) Length of rectangular part = 50 cm Breadth = Diameter of semi- circle = 2(35 cm) = 70 cm Area of rectangular part = \(length \times \breadth\) = \(50 \times 70\) = \(3500 cm^{2}\) Total area of window = \((3500 + 1925) cm^{2}\) = \(5425 cm^{2}\)
