Let x and y be the two numbers. Their average is
[tex]\dfrac{x+y}{2}=20 \iff x+y=40[/tex]
If we multiply x and y be 2 and 3, respectively, the average becomes
[tex]\dfrac{2x+3y}{2}=52 \iff 2x+3y=104[/tex]
We can use the two equations to make a linear system:
[tex]\begin{cases}x+y=40\\2x+3y=104\end{cases}[/tex]
From the first equation we can derive
[tex]x=40-y[/tex]
Plug this value in the second equation and we have
[tex]2(40-y)+3y=104 \iff 80-2y+3y=104 \iff y=24[/tex]
Now recall the relation between x and y to conclude
[tex]x=40-y=40-24=16[/tex]
So, the two numbers are 16 and 24
On solving the linear system [tex]\rm x + y = 40[/tex] and [tex]\rm 2x + 3y = 104[/tex]. Then the value of x and y whose average be 20 is 16 and 24.
It is a system of an equation in which the highest power of the variables is always 1. A one-dimension figure that has no width. It is a combination of infinite points side by side.
Given
The average of two numbers is 20.
One of the numbers is doubled and the other is trebled the average increase to 52.
Let the numbers be x and y.
According to the first condition.
[tex]\rm \dfrac{x+y}{2} = 20[/tex]
On simplifying
[tex]\rm x + y = 40[/tex].....(1)
According to the second condition.
[tex]\rm \dfrac{2x+3y}{2} = 52[/tex]
On simplifying
[tex]\rm 2x + 3y = 104[/tex].....(2)
From equations 1 and 2, we get the numbers
x = 16 and y = 24.
Thus, the numbers are 16 and 24.
More about the linear system link is given below.
https://brainly.com/question/20379472
