Question

A number X equals 80% of the average of 5, 7, 14 and a number Y. If the average of X and Y is 26, the value of Y is?


Kindly, tell me how this question will be solved, please.

Thank you.

Answer 1

Well, this question has a pretty simple solution.

You need to create the system of equations,

The first equation will be as follows:

$x=0.8*\dfrac{5+7+14+y}{4}$

The second equation will be as follows:

$\dfrac{x+y}{2}=26$

Now let's just solve this system:

$\begin{cases} x=0.8*\dfrac{5+7+14+y}{4} \\ \dfrac{x+y}{2}=26 \end{cases}$

$\begin{cases} x=0.2*(26+y) \\ \dfrac{x+y}{2}=26 \end{cases}$

Let's substitute x from the first equation into the second one:

$\begin{cases} x=0.2*(26+y) \\ \dfrac{(0.2*(26+y)+y)}{2}=26 \end{cases}$

Now simply solve the second equation:

$\dfrac{(0.2*(26+y)+y)}{2}=26$

0.2 * (26 + y) + y = 26*2

5.2 + 0.2y + y = 52

1.2y = 52 - 5.2

1.2y = 46.8

y = 46.8 / 1.2

y = 39