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

I may or may not be wrongBut36 femalesBecause There are 48 all together1/3 question 12 males48 females...

The average of two real numbers is 12.75 and their

dodsonh16

13.03.2022

12.5 and 13

Step-by-step explanation:

Let the numbers are x and y,

So, their average = $\frac{x+y}{2}$

And, their product = xy

According to the question,

$\frac{x+y}{2}=12.75$

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

Also,

xy = 162.5

$\implies x =\frac{162.5}{y}----(2)$ ,

From equation (1) and (2),

$\frac{162.5}{y}+y=25.5$

162.5+y^2 = 25.5y

y^2 - 25.5y + 162.5 = 0

By quadratic formula,

$y=\frac{25.5\pm \sqrt{(-25.5)^2 -4\times 1\times 162.5}}{2}$

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

From equation (1),

If y = 12.5,x = 13

If y = 13, x = 12.5

Hence, numbers are 12.5 and 13

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