WAEC Mathematics 2020 Theory — Question 8

Model answer

(a)(i) Let her total income be #x. Fraction spent on food = 1/4, fraction spent on open market = 1/3. Note the addition of all fractions must equal 1; let the remaining fraction (before mechanic workshop spend) be a: 1/4+1/3+a=1 => 7/12+a=1 => a=5/12. So, if the woman spends 2/3 of the remaining fraction (5/12) on mechanic workshop, the fraction spent on mechanic workshop = 2/3 of 5/12 = 2/5 x 5/12 = 1/6. Fraction saved = remaining fraction - fraction spent on workshop = 5/12-1/6=1/4. From the equation, the saved income = #225,000: 1/4 x #x = #225,000, so x=#900,000. Therefore, the woman's total income is #900,000. (ii) Amount spent on open market = fraction of open market x Total income = 1/3 x #900,000 = #300,000. (b) The nth term of an AP is given by Tn=a+(n-1)d, where a=first term, d=common difference. For the 3rd term: T3=a+2d=4m-2n. For the 9th term: T9=a+8d=2m-8n. Subtracting: (a+8d)-(a+2d)=(2m-8n)-(4m-2n) => 6d=-2m-6n. Dividing both sides by 6: d=(-1/3)(m+3n).