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GCSE Mathematics Problem: Handling Data Higher Tier - Algebra to Help Solve

Get a helping hand with GCSE Mathematics problem solving by using algebra. This problem involves finding six numbers given certain statements and data. Work through each statement to gather additional information and solve the problem.

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GCSE Mathematics Problem: Handling Data Higher Tier - Algebra to Help Solve

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  1. GSCE Mathematics Problem Solving Handling Data Higher Tier

  2. Helping hand Use algebra to help you. Let the first number be a. Work through each statement to get additional information. 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.

  3. Answer Let the 1st number be a The 2nd number is double the 1st number so 2a The 3rd 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: 6th number – 1st number = 33 so 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 Half way 2a 29 ___ 2a+20 33+a a 3 values are above this & 3 are below.

  4. a 2a 29 32 2a+20 33+a The mean is 28, so: a + 2a + 29 + 32 + 2a+20 + 33+a = 28 6 a + 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

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