GSCE Mathematics Problem Solving Handling Data Higher Tier

Lily chooses the same numbers for the National Lottery every week. Unfortunately, she has forgotten all but one of her numbers. If the six numbers are written in ascending order and given that:  the second number is double the first number  the third number is 29  the fifth number is twenty more than the second number  the range of the six numbers is 33  the median is 30.5  the mean is 28 Find all of the numbers. Helping hand Use algebra to help you. Let the first number be a. Work through each statement to get additional information.

2a 29 ___ 2a a Answer Let the 1 st number be a The 2 nd number is double the 1 st number so 2a The 3 rd number is 29 The fifth number is twenty more than the second number so 2a + 20 The range of the six numbers is 33, so: 6 th number – 1 st number = 33 so6 th number = st number = 33 + a The median is 30.5, which lies between the 3 rd and 4 th values. The mean of these two values is 30.5, so they must total 61. So the 4 th value is 61 – 29 = 32 a Half way 3 values are above this & 3 are below.

 a 2a a a The mean is 28, so: a + 2a a a = 28 6 a + 2a a a = 168 6a = 168 6a = 54 a = 9 So if a =9, 2a = 18, 2a + 20 = 38, 33 + a = 42 9,18,29,32,38,42