Question

If 28x+22y=50 and 22x+28y=150 then x+y is equals to?
(a) 2
(b) 1
(c) 4
(d) 200

Answer 1

First, before proceeding for this, we must know that the two variables equations are given which are two in number, so that we can easily calculate the value of x and y. Then by using the substitution method which says that to substitute one variable value from one equation to another to get the other variable value and by following it, we get the value of x and y. Then, by using the values calculated, we get the value of the expression x+y as a result.

Complete step by step answer:
In this question, we are supposed to find the value of x+y when two equations are given as 28x+22y=50 and 22x+28y=150.
So, before proceeding for this, we must know that the two variables equations are given which are two in number, so that we can easily calculate the value of x and y.
Now, by using the substitution method which says that to substitute one variable value from one equation to another to get the other variable value.
So, by using this concept, find the value of x from first equation given in question which is 28x+22y=50 in terms of y as:
$\begin{aligned} & 28x=50-22y \\\ & \Rightarrow x=\dfrac{50-22y}{28} \\\ \end{aligned}$
Now, by substituting the value of x obtained in the second question in the question which is 22x+28y=150, we get:
$22\left( \dfrac{50-22y}{28} \right)+28y=150$
Now, we get the expression in single variable and by solving it we get the value of y as:
$\begin{aligned} & 22\left( \dfrac{50-22y}{28} \right)+28y=150 \\\ & \Rightarrow \dfrac{22}{28}\times 50-\dfrac{22}{28}\times 22y+28y=150 \\\ & \Rightarrow 39.29-17.29y+28y=150 \\\ & \Rightarrow 10.71y=110.71 \\\ & \Rightarrow y=\dfrac{110.71}{10.71} \\\ & \Rightarrow y=10.34 \\\ \end{aligned}$
Then, by substituting the value of y as 10.34 in the first equation which is 28x+22y=50 to get the value of x as:
$\begin{aligned} & 28x+22\left( 10.34 \right)=50 \\\ & \Rightarrow 28x+227.48=50 \\\ & \Rightarrow 28x=-177.48 \\\ & \Rightarrow x=\dfrac{-177.48}{28} \\\ & \Rightarrow x=-6.34 \\\ \end{aligned}$
So, we get the value of x as -6.34 and value of y as 10.34.
Now, by using these values, we get the value of expression x+y as:
$\begin{aligned} & x+y=-6.34+10.34 \\\ & \Rightarrow 4 \\\ \end{aligned}$
So, we get x+y as 4.

Hence, option (c) is correct.

Note:
Now, to solve these types of questions we need to know some of the other methods also to solve these types of two variable equations which are elimination method and cross multiplication method. So, we can also use these two methods to get the value of x and y.