.
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?
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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.
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