GSCE MathematicsProblem Solving

Handling DataHigher 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 handUse algebra to help you.

Let the first number be a.Work through each statement to get additional information.

2a 29 ___ 2a+20 33+a

AnswerLet the 1st number be aThe 2nd number is double the 1st number so 2aThe 3rd number is 29The fifth number is twenty more than the second number so 2a + 20The range of the six numbers is 33, so:

6th number – 1st number = 33so 6th number = 33 + 1st number = 33 +

a

The median is 30.5, which lies between the 3rd and 4th values. The mean of these two values is 30.5, so they must total 61. So the 4th value is 61 – 29 = 32

a

Half way

3 values are above this & 3 are

below.

a 2a 29 32 2a+20 33+a

The mean is 28, so:a + 2a + 29 + 32 + 2a+20 + 33+a = 28

6a + 2a + 29 + 32 + 2a+20 + 33+a = 168

6a + 114 = 168 6a = 54

a = 9

So if a =9, 2a = 18, 2a + 20 = 38, 33 + a = 42

9, 18, 29, 32, 38, 42