In: Statistics and Probability
A mixture of 27 units of fertilizer A, 67 units of fertilizer B, and 22 units of fertilizer C provides the optimal nutrients for a crop to grow. Each pound of brand X provides 1 unit of fertilizer B and 1 unit of fertilizer C. Each pound of brand Y provides 1 unit of A and 2 units of B. Each pound of brand Z provides 2 units of A, 5 units of B, and 2 units of C. How many pounds of each fertilizer brand should be bought in order to obtain the desired mixture?