Question

The mean of: a, a, b is 30

the mean of a, a, b, b, b, is 20
find the values of a and b

Answer 1

a+b = 40

Explanation:

Mean of a and b is [math]\frac{a+b}{2} = 20[/math]

[math]

Answer 2

a is 42.5

b is 5

Explanation:

the mean of: a, a, b is 30

`(a + a + b)/(3) = 30`

`(2a + b)/(3) = 30`

multiply 3 on both sides

`2a + b = 90`

the mean of a, a, b, b, b, is 20

`(a + a + b + b + b)/(5) = 20`

`(2a + 3b)/(5) = 20`

multiply 5 on both sides

`2a + 3b = 100`

solve both equations simultaneously

`2a + b = 90`

`2a + 3b = 100`

subtract across. 2a-2a=0, b-3b= -2b, 90-100= -10

`- 2b = - 10`

`b = 5`

go back to one of the equations and substitute b=5 back in to find a

`2a + b = 90`

`2a + 5 = 90`

subtract 5 on both sides

`2a = 85`

divide 2

`a = 42.5`

so a is 42.5 and b is 5