Question

A shirt cost Rs.12 more than 1 belt. The total cost of 2 such shirts and 5 such belts is Rs. 164. What is the cost of one belt?
A) Rs. 20
B) Rs. 22
C) Rs. 32
D) Rs. 34

Answer 1

Hint: A linear system of two equations with two variables is any system that can be written in the form.
\[
  ax + by = p \\
  cx + dy = q \\
 \]
where any of the constants can be zero with the exception that each equation must have at least one variable in it. Use the Linear equation with two variables to solve the question.

Complete step by step solution:
Let the cost of shirt be = $x$
The cost of belt is = $y$
So the first equation as per the given condition a shirt cost Rs.12 more than 1 belt, is
\[ \Rightarrow x = 12 + y\] …… (1)
The second equation is as per the given condition the total cost of 2 such shirts and 5 such belts is Rs. 164 is
\[ \Rightarrow 2x + 5y = 164\] ………(2)
Using the method of substitution, using values of $x$ from equation (1) and putting in equation (2),
While solving the equation we just have to remember, no matter what kind of equation we're dealing with — linear or otherwise — whatever we do to the one side of the equation, we must do the exact same thing to the other side of the equation.
\[ \Rightarrow 2\left( {12 + y} \right) + 5y = 164\]
So, now the given equation is a linear equation in one variable with the variable as ‘$y$’. So, we need to find out the value of ‘$y$’.
Expanding all the brackets in the above equation.
\[ \Rightarrow 24 + 2y + 5y = 164\]
Grouping the like terms together and simplifying the equation.
\[ \Rightarrow 7y = 164 - 24\]
\[ \Rightarrow y = \dfrac{{140}}{7}\]
\[ \Rightarrow y = 20\]

So, the cost of one belt is Rs. 20. Option A is the correct answer.

Note:
Solving linear equations is all about isolating the variable. Depending on the equation, this may take as little as one step or many more steps. Always check if you need to simplify one or both sides of the equation first, and always check your answer.