Question

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?

Answer 1

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.

Answer 2

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.