Question

Twenty pillows can be bought for Rs. 5120. How many pillows can be bought for Rs. 7936?

Answer 1

Hint: In this question, we need to assume the cost of each pillow as some x and then find the cost of each pillow using the equation formed of the cost of twenty pillows. Then assume that y pillows can be brought with Rs. 7936 and then dividing it with the cost of each pillow gives the answer.

Complete step-by-step solution -
Let us first look at some of the 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 \[ax+by+c=0\] .
Equation’s solution : 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, from the given question let us assume that the cost of each pillow as x.
\[\begin{align}
  & \Rightarrow 20\times x=5120 \\
 & \Rightarrow x=\dfrac{5120}{20} \\
 & \Rightarrow x=\dfrac{512}{2} \\
 & \therefore x=256 \\
\end{align}\]
Hence, the cost of each pillow is Rs.256
Now, let us assume that y pillows can be brought with Rs.7936 we get,
\[\begin{align}
  & \Rightarrow 256\times y=7936 \\
 & \Rightarrow y=\dfrac{7936}{256} \\
 & \Rightarrow y=\dfrac{31\times 256}{256} \\
 & \therefore y=31 \\
\end{align}\]
Hence, with Rs.7936 we can buy 31 pillows.

Note: Instead of assuming that the cost of each pillow as x we can directly solve it by using the cross multiplication method in which we consider if the cost of 20 pillows is Rs. 5120 then how many pillows would cost Rs. 7936. Then simply it is as follows.
Number of pillows can be brought with Rs.7936 is:
\[\begin{align}
  & \Rightarrow \dfrac{7936\times 20}{5120} \\
 & \Rightarrow \dfrac{31\times 256\times 2}{2\times 256} \\
 & \Rightarrow 31 \\
\end{align}\]
Thus, it gives the same result.
It is important to note that while finding x it gives the value of each pillow because we already know that there are twenty pillows. But, in the second case here we are finding the number of pillows unlike the cost of a pillow. So, we need to use that cost of pillow obtained in that case to get the number of pillows in this case.