Example 4
Assignment. A company has two filter types in storage, but the unit prices for the filters are missing. According to the logs, the company bought 50 type A filters and 100 type B filters on January, with a total cost of 450 euros. On February, the company bought 30 type A filters and 40 type B filters, with a total cost of 200 €. Use this information to recover the unit prices for each filter.
Solution. Let us denote the unit prices (for filter A) and (for filter B). If we buy 50 type A filters, their price is , and if we buy 100 type B filters, their price is . Therefore, the total costs for January can be expressed with the equation
and similarly for February. We obtain a pair of equations:
Let us multiple the equations so that the coefficients of are opposite numbers:
Adding rows 1 and 2 yields
Substituting this on the 1st row yields
The unit prices are 2 euros for filter A, and 3,5 euros for filter B.