text: 1)A number is divided into 2 parts such that one is 10 more than the other. if the 2 parts are in the ratio 5:3, find the number.\n\nLet the smaller part be n. Therefore the other part is n + 10\n(n + 10)/n = 5/3\nMultiply by n\nn + 10 = 5n/3\nMultiply by 3\n3(n + 10) = 5n\nTherefore 3n + 30 = 5n\nTake 3n from both sides\n30 = 2n \nSo n = 15 and n + 10 = 25 \nSo the original number was 15 + 25 = 40\n\n2)if 1/2 is substracted from a number and the difference is multiplied by 4 the result is 5, find the number.\nLet the number be n\nThus the difference = n - 1/2\n4(n - 1/2) = 5\nSo 4n - 2 = 5\nAdd 5 to both sides\n4n = 7\nn = 7/4\n= 1 3/4\n\n3)Jane and Jean start walking from the same place in opposite directions. If Jane walks at a speed of 2 and 1/2 km per hourand Jean at 2 km /per hour, in how much time will they be 18 km apart?\n\nLet them walk for t hours\nIn this time Jane walks 2 1/2 t km ie 5t/2 km\nand Jean walks 2t km\nSo they are (2t + 5t/2) km apart\n\nSo 2t + 5t/2 = 18\nMultiply everything by 2\n4t + 5t = 36\nie 9t = 36\nSo t = 4\nie it takes 4 hours for them to be 18 km apart