SOLUTION: How many gallons of a plant food that is 9% nitrogen must be combined with another plant food that is 25% nitrogen to make 10 gal of a plant food that is 13% nitrogen?

Let "x" = the amount of the plant food that is 9% nitrogen under the question, in gallons.
Then the amount of the plant food that is 25% nitrogen is (10-x) gallons.

The amount of the pure nitrogen in the solution/mixture is 

0.09*x + 0.25*(10-x).

It should be equal to 0.13*10, which gives you an equation

0.09*x + 0.25*(10-x) = 0.13*10,  or

0.09x + 2.5 - 0.25x = 1.3,  or

-0.16x = 1.3 - 2.5,  or

-0.16x = -1.2.

Hence, x =  =  =  = 7.5.

Thus we just found the volume  of the plant food that is 9% nitrogen is 7.5 gallons.

Check. 0.09*7.5 + 0.25*(10-7.5) = 1.3.

        = 0.13 = 13%.  Correct !


Anwser.  The volume of the plant food that is 9% nitrogen is 7.5 gallons.