Question

The mean of a set of 6 number is 2 and the mean of another set of 10 number is x.if the mean of all 16 number is 7 find the value of c.

​

Answer 1

x = 10

Explanation:

Let the sum of first 6 numbers be
`\text{s}_(6)`

Let the sum of next 10 numbers be
`\text{s}_(10)`

Given:

`\frac{\text{s}_(6)}{6} = 2 ,\;\;\;\;\frac{\text{s}_(10)}{10} = x\\\\\Rightarrow \text{s}_(6) = 2*6 \;\;\;\text{and}\;\;\;\text{s}_(10) =10x\\\\\Rightarrow \text{s}_(6) = 12 \;\;\;\text{and}\;\;\;\text{s}_(10) =10x`

Also,

`\frac{\text{s}_(6)+\text{s}_(10)}{16} = 7\\\\\Rightarrow (12 + 10x)/(16) = 7\\\\\Rightarrow 12 + 10x= 16*7\\\\\Rightarrow 12 + 10x= 112\\\\\Rightarrow 10x= 112-12\\\\\Rightarrow 10x= 100\\\\\Rightarrow x = (100)/(10)\\ \\\Rightarrow x = 10`