Question

The average of two real numbers is 12.75 and their product is 162.5. what are the numbers?

Answer 1

.5(x+y)=12.75
x*y=162.5 isolate y
y=162.5/x plug in 1st equation
.5(x+162.5/x)=12.75
.5x+81.25/x-12.75=0
.5x^2-12.75x+81.25=0
x=13 and 12.5

Answer 2

12.5 and 13

Explanation:

Let the numbers are x and y,

So, their average =
`(x+y)/(2)`

And, their product = xy

According to the question,

`(x+y)/(2)=12.75`

`x+y = 25.5-----(1)`

Also,

xy = 162.5

`\implies x =(162.5)/(y)----(2)`,

From equation (1) and (2),

`(162.5)/(y)+y=25.5`

`162.5+y^2 = 25.5y`

`y^2 - 25.5y + 162.5 = 0`

By quadratic formula,

`y=(25.5\pm √((-25.5)^2 -4* 1* 162.5))/(2)`

`\implies y = 12.5\text{ or }y = 13`

From equation (1),

If y = 12.5,x = 13

If y = 13, x = 12.5

Hence, numbers are 12.5 and 13