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

The correct option is D The given situation describes an impossible situationWe 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 a1a2=b1b2≠c1c2i.e405=204≠13028. Therefore the equations when plotted on a graph shows that the lines are parallel and hence describes an impossible situation.

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