A box of pencils costs the same as 11 erasers and 7 pencils

A box of pencils costs the same as 11 erasers and 7 pencils. A box of erasers costs the same as 6 erasers and a pencil. A box of empty boxes and an eraser costs the same as a pencil. Given that boxes cost a penny and each of the boxes contain an equal number of objects, how much does it costs to buy a box of pencils and a box of erasers combined?

Solution

If you consider the cost of the box to be added to the cost of its contents, and if you let e, p, and n represent the cost of erasers, the cost of pencils, and the number of objects in a box, respectively, you can write these equations:
.. n + e = p ... (n-1) boxes and an eraser in a box costs the same as a pencil
.. np + 1 = 11e + 7p ... a box of pencils costs the same as 11 erasers and 7 pencils
.. ne + 1 = 6e + p ... a box of erasers costs the same as 6 erasers and a pencil

Rounded to 2 decimal places, the \"reasonable\" solutions to these equations are
.. e = 3.24, p = 12.92, n = 9.68
There are no integer solutions.