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?

• A. Notebook is $\$2.50$ and newspaper is $\$1.50$
• B. Notebook costs $\$1.50$ and newspaper is $\$2.50$
• C. There is not enough information to determine the exact costs
• D. The given situation describes an impossible situation

Answer 1

The correct option is D The given situation describes an impossible situation

We form the two equations from the information given as follows :
Let ‘b’ be the cost of a notebook and ‘n’ be the cost of a newspaper.
Therefore $40b+20n=130$ ....... (i)
$8b+4n=28$ ....... (ii)
From the above two equations we can compare the ratio of the coefficients of x and y and also the constant, which indicates $\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}i.e\frac{40}{5}=\frac{20}{4}\ne \frac{130}{28}$. Therefore the equations when plotted on a graph shows that the lines are parallel and hence describes an impossible situation.