SOLUTION: A mixture of 10 pounds of fertilizer A, 25 pounds of fertilizer B, and 7 pounds of fertilizer C provides the optimal nutrients for a plant. Commercial brand X contains equal parts

Let x be the amount of the brand X, in pounds;

    y be the amount of the brand Y, in pounds,  and

    z be the amount of the brand Z, in pounds.



    Notice that I use small letters x, y and z for amounts of the corresponding brands X, Y and Z, 
    so do not miss the small and capital letters --- they have different appearance and different meaning (!)


Then the amount of the fertilizer A in the mixture is   +  =  +  pounds.

It gives you your first equation

     +  = 10   pounds of fertilizer A    (1)



Next, the amount of the fertilizer B in the mixture is   +  +  =  +  +  pounds.

It gives you your second equation

     +  +  = 25   pounds of fertilizer B    (2)



Finally, the amount of the fertilizer C in the mixture is   +  =  +  pounds.

It gives you your third equation

     +  =  7   pounds of fertilizer C    (3)



Thus you have this system of 3 equations in 3 unknown

           +  = 10       (1)

     +  +  = 25       (2)

           +  =  7       (3)


At this point, the setup is just completed.
Now your task is to solve the system and to find the values of unknowns x, y, and z.


It could be done by different ways, using different methods.
But the first step I recommend is to rid of the denominators.
For it, multiply eq(1) by 9 (both sides); eq(2) by 18 and eq(3) by 18, again.  
You will get then equivalent system of equations with integer coefficients 

          3y +  2z =  90       (1')

    9x + 12y + 10z = 450       (2')

    9x +        4z = 126       (3')   


As I just said above, you can solve it using different methods.

For example, Elimination method would work nicely.


But in order for to save my time, I will use online solver and only will give you the answer from this solver.


ANSWER.  6, 18 and 18 pounds of the brands X, Y and Z respectively.