Question

In Shimla, on Tuesday the temperature was\[-{{8}^{\circ }}C\]. It then dropped by \[{{4}^{\circ }}C\] on Wednesday. On Thursday, it raised by x. If the temperature on Thursday is\[-{{7}^{\circ }}C\], then find the value of x.
(a) \[{{4}^{\circ }}C\]
(b)\[{{5}^{\circ }}C\]
(c) \[{{7}^{\circ }}C\]
(d) \[{{2}^{\circ }}C\]

Answer 1

Hint: In this question, we first need to look at some basic definitions of algebra. Then from the temperature on Tuesday we need to subtract the drop on Wednesday then we need to add the raise to it and equate to the temperature on Thursday.

Complete step-by-step answer:
Let us look at some basic definitions of algebra.
LINEAR EQUATIONS:
Equation: A statement of equality of two algebraic expressions involving two or more unknown variables is called equation.
Linear Equation: An equation involving the variables in maximum of order 1 is called a linear equation. Graph of a linear equation is a straight line.
Linear equation in one variable is of the form \[ax+b=0\].
Linear equation in two variables is of the form \[ax+by+c=0\] .
Solution of an Equation- A particular set of values of the variables, which when substituted for the variables in the equation makes the two sides of the equation equal, is called the solution of the equation.
Simultaneous Linear Equation- A set of linear equations in two variables is said to form a system of simultaneous linear equations, if both equations have the same solution.
Consistency of Simultaneous Linear Equation: If a system of simultaneous linear equations has at least one solution, then the system of linear equations is called consistent.
Inconsistency of Simultaneous Linear Equation: If a system of simultaneous linear equations has at least no solution, then the system of linear equations is called inconsistent.

Now, let us assume that the temperature on Wednesday as y.
\[\Rightarrow y=-8-\left( 4 \right)\]
\[\therefore y=-{{12}^{\circ }}C\]
Temperature on Thursday can be written as:
\[\Rightarrow y+x\]
As we already know that temperature on Thursday is \[-{{7}^{\circ }}C\]we get,
\[\begin{align}
  & \Rightarrow y+x=-7 \\
 & \Rightarrow -12+x=-7\text{ }\left[ \because y=-12 \right] \\
 & \Rightarrow x=12-7 \\
 & \therefore x={{5}^{\circ }}C \\
\end{align}\]
Hence, the correct option is (b).

Note: Instead of considering some variable for temperature on Wednesday we can directly calculate it and then add x to it and equate it to the given temperature on Thursday. Both ways give the same result. It is just that we do not assume any variable in this case.
While solving the question to get the temperature on Wednesday we need to subtract the given value from the temperature on Tuesday because it is a drop. Similarly while calculating the temperature on Thursday we need to add the given value to the temperature on Wednesday because there is a raise.