Question

A mixture of 5 pounds of fertilizer A, 13 pounds of fertilizer B, and 4 pounds of fertilizer C provides the optimal nutrients for a plant. Commercial brand X contains equal parts of fertilizer B and fertilizer C. Commercial brand Y contains one part of fertilizer A and two parts of fertilizer B. Commercial brand Z contains two parts of fertilizer A, five parts of fertilizer B, and two parts of fertilizer C. How much of each fertilizer brand is needed to obtain the desired mixture? (If the system is dependent enter a for brand X and enter brand Y and brand Z in terms of a.)

Answer 1

x = 2; y = 3; z = 1

Explanation:

For the first fertilizer (A) we can form the equation:

y + 2z = 5

For the second fertilizer (B) we can form the equation:

x + 2y + 5z = 13

For the third fertilizer (C) we can form the equation:

x + 2z = 4

solving simulteneously:

y = 5 - 2z

x = 4 -2z

Substituting (i) and (ii) into (2)

4 - 2z + 10 -4z + 5z = 13

14-z =13, therefore z = 1

substituting z into (i) and (ii)

y = 3

x = 2