What is the cost of one pencil and one notebook if a student sold twelve pencils and eleven notebooks and got a total of twenty eight dollars solved with a system of equations?

Answer 1

The equation to solve is 12p + 11n = 2800 (where p is the cost of a pencil and n is the cost of a notebook and $28 is expressed as 2800 cents).

Make n the subject:

n = (2800-12p)/11.

This is called a diophantine equation as it has lots of solutions.

There are 21 different solutions to this equation:

6c for a pencil and $2.48 for a notebook. Total for one of each is $2.54

17c for a pencil and $2.36 for a notebook. Total for one of each is $2.53

28c for a pencil and $2.24 for a notebook. Total for one of each is $2.52

39c for a pencil and $2.12 for a notebook. Total for one of each is $2.51

50c for a pencil and $2.00 for a notebook. Total for one of each is $2.50

61c for a pencil and $1.88 for a notebook. Total for one of each is $2.49

72c for a pencil and $1.76 for a notebook. Total for one of each is $2.48

83c for a pencil and $1.64 for a notebook. Total for one of each is $2.47

94c for a pencil and $1.52 for a notebook. Total for one of each is $2.46

There are 12 more answers.

The last answer in this series is $2.26 for pencil and 8c for a notebook. Total for one of each is 2.34

But not all of them are practical e.g. the last one.