(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 > 7frac{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})