We can see that there can be many possible values for the price of a notebook and of a pen
so that the total cost is `80. So, how do we find the price at which Siri and Laxmi bought them?
By using only Siri's situation, we cannot find the costs. We have to use Laxmi's situation also.
4.1.2 USING BOTH EQUATIONS TOGETHER
Laxmi also bought the same types of notebooks and pens as Siri. She paid `110 for 4
notebooks and 3 pens.
So, we have two situations which can be represented as follows:
(i) Cost of 3 notebooks + 2 pens = `80.
(ii) Cost of 4 notebooks + 3 pens = `110.
Does this help us find the cost of a pen and a notebook?
Consider the prices mentioned by Rubina. If the price of one notebook is `25 and the
price of one pen is `2.50 then,
The cost of 4 notebooks would be : 4 × 25 = `100
And the cost for 3 pens would be : 3 × 2.50 = `7.50
If Rubina is right then Laxmi should have paid ` 100 + ` 7.50 = ` 107.50 but she paid `110.
Now, consider the prices mentioned by Joseph.
The cost of 4 notebooks, if one is for `16, would be : 4 × 16 = ` 64
And the cost for 3 pens, if one is for `16, would be : 3 × 16 = ` 48
If Joseph is right then Laxmi should have paid `64 + `48 = `112 but this is more than the
price she paid.
So what do we do? How to find the exact cost of the notebook and the pen?
If we have only one equation but two unknowns (variables), we can find many solutions.
So, when we have two variables, we need at least two independent equations to get a unique
solution. One way to find the values of unknown quantities is by using the Model method. In this
method, rectangles or portions of rectangles are often used to represent the unknowns. Let us
look at the first situation using the model method:
Step-1 : Represent a notebook by and a pen by .
Siri bought 3 books and 2 pens for `80.
Laxmi bought 4 books and 3 pens for `110.