Liam's bookstore sold 40 notebooks and 20 newspapers for a total of $130. A day later, the bookstore sold 8 notebooks and 4 newspapers at the same prices, for a total of $28. How much does a notebook and a newspaper cost at Liam's bookstore?

The total sales will be calculated by adding up the revenue from the selling of the notebooks and that of the newspaper. For representation, we let x be the price of each of the notebook and y be the price of each of the newspaper. The equation that allows us to solve this item are,

40x + 20y = 130

and 8x + 4y = 28

With this, if we divide the left hand side by the left hand side of the equation number 2, we have 5. However, 130 divided 28 is not 5 but 4.64. Hence, the system does not have any solution.

Let us say that:

X = price of each notebook

Y = price of each newspaper

So from the problem statement we can create the following equations:

40 X + 20 Y = 130 - - > eqtn 1

8 X + 4 Y = 28 - - > eqtn 2

Divide both equations by the lowest coefficient to simplify:

Divide eqtn 1 by 20 = > 2 X + Y = 6.5

Divide eqtn 2 by 4=> 2 X + Y = 7

So we can see that although both equations has equal left side, the right side do not match. Hence this problem is impossible to solve.

-> The given information describes an impossible situation.