WAEC Mathematics 2019 Theory — Question 4

Model answer

(a) Total ratio = 3+5+8 = 16. Ali's share = 3/16×420,000 = #78,750. Yusif's share = 8/16×420,000 = #210,000. Sum of Ali and Yusif's shares = #78,750 + #210,000 = #288,750. (b) 2(1/8)ˣ = 32ˣ⁻¹ ⇒ 2(8⁻¹)ˣ = 32ˣ⁻¹ ⇒ 2(8)⁻ˣ = 32ˣ⁻¹. Since 8=2³ and 32=2⁵: 2(2³)⁻ˣ = (2⁵)ˣ⁻¹ ⇒ 2¹(2)⁻³ˣ = 2⁵ˣ⁻⁵ ⇒ 2¹⁻³ˣ = 2⁵ˣ⁻⁵. Equating powers: 1−3x = 5x−5 ⇒ 1+5 = 5x+3x ⇒ 6=8x ⇒ x = 6/8 = 3/4 = 0.75.