GCE Mathematics 2022 Theory — Question 2

Model answer

Let the numbers be a and b, with a:b = 3:4, so b = (4/3)a. Thrice the first plus twice the second = 68: 3a + 2b = 68. Substituting b = (4/3)a: 3a + 2(4/3)a = 68, i.e. 3a + 8a/3 = 68. Multiply through by 3: 9a + 8a = 204, so 17a = 204, giving a = 12. Since a:b = 3:4 and a=12, b=16 (check: 3(12)+2(16)=36+32=68, correct). The smaller number is 12.