Question

The sum of 5 numbers is 825 the average of the first two numbers is 196.5 and the average of the last two numbers is 186 what is the third number

Answer 1

Answer:   third number is 60

Step-by-step explanation:

let the numbers be : p, q, r, s, t

we know : p+q+r+s+t = 825

dividing by 2

$\frac{p+q+r+s+t}{2} = \frac{825}{2}$

$\frac{p+q}{2} + \frac{r}{2} + \frac{s+t}{2} = 412.5$

given : avg of first 2 numbers: $\frac{p+q}{2} = 196.5$

           avg of last 2 numbers: $\frac{s+t}{2} = 186$

∴$196.5 + \frac{r}{2} + 186 = 412.5\\\frac{r}{2} = 412.5 - 196.5 - 186\\\frac{r}{2} = 30$

∴ r = 60

thus 3rd number is 60

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