(a) An open rectangular tank is made of a steel plate of area 1440(m^{2}). Its length is twice its width . If the depth of the tank is 4m less than its width, find its length.
(b) A man saved N3,000 in a bank P, whose interest rate was x% per annum and N2,000 in another bank Q whose interest rate was y% per annum. His total interest in one year was N640. If he had saved N2,000 in P and N3,000 in Q for the same period, he would have gained N20 as additional interest. Find the values of x and y.
Explanation
(a) Width = x m; Length = 2x m; Height = (x – 4) m.
Total surface area = 2Lh + WL + 2Wh
= (2(2x)(x – 4) + x(2x) + 2(x)(x – 4) = 1440 m^{2})
= (4x^{2} – 16x + 2x^{2} + 2x^{2} – 8x = 1440)
= (8x^{2} – 24x = 1440)
= (x^{2} – 3x – 180 = 0)
= ((x – 15)(x + 12) = 0)
(x = 15m)
Length = 2(15m) = 30m.
(b) (I = frac{PRT}{100})
(I_{P} + I_{Q} = I_{T})
(frac{3000 times x times 1}{100} + frac{2000 times y times 1}{100} = 640)
(30x + 20y = 640 implies 3x + 2y = 64 …. (1))
(frac{2000 times x times 1}{100} + frac{3000 times y times 1}{100} = 660)
(20x + 30y = 660 implies 2x + 3y = 66 …. (2))
To eliminate x , multiply (1) by 2 and (2) by 3.
(6x + 4y = 128 … (1))
(6x + 9y = 198 …. (2))
(2) – (1) : (9y – 4y = 198 – 128 implies 5y = 70)
(y = 14)
(2x + 3y = 66 implies 2x + 3(14) = 66)
(2x + 42 = 66 implies 2x = 24)
(x = 12)
(therefore x = 12 ; y = 14).