(a) A shop owner marked a shirt at a price to enable him to make a gain of 20%. During a special sales period, the shirt was sold at 10% reduction to a customer at N864.00. What was the original cost to the shop owner?
(b) A rectangular lawn of length (x + 5) metres is (x – 2) metres wide. If the diagonal is (x + 6) metres, find ;
(i) the value of x ; (ii) the area of lawn.
Explanation
(a) Price with 20% gain = 100% = x
Selling price = 100% – 10% = 90%
i.e. 90% of x = 864
(therefore x = 864 times frac{100}{90} = N960)
Let cost price = y = 100%
x = 20% of y + y = 120% of y.
(y = frac{100}{120} x = frac{100}{120} times N960 = N800)
(b)
(i) ((x + 6)^{2} = (x + 5)^{2} + (x – 2)^{2})
(x^{2} + 12x + 36 = x^{2} + 10x + 25 + x^{2} – 4x + 4)
(x^{2} + 12x + 36 = 2x^{2} + 6x + 29)
(2x^{2} – x^{2} + 6x – 12x + 29 – 36 = 0)
(x^{2} – 6x – 7 = 0)
(x^{2} – 7x + x – 7 = 0 implies x(x – 7) + 1(x – 7) = 0)
((x – 7)(x + 1) = 0 implies text{x = 7 or -1})
Since measurements cannot be negative, then x = 7 is the suitable answer.
(ii) Length of the lawn = (x + 5) metres = (7 + 5) = 12 metres.
Width of the lawn = (x – 2) metres = (7 – 2) = 5 metres
(therefore text{The area of the lawn} = 12 times 5 = 60 m^{2})