Mixing Fertilizer

Question

Yard bird Gardening carries two
kinds of fertilizer containing nitrogen and water. “Gently Green” is 5% nitrogen
and “Sun Saver” is 15% nitrogen. Yard bird Gardening needs to combine the two
types of solution to make 90 L of a solution that is 12% nitrogen. How much of
each brand should be used?

Answer 1

Before starting this problem, I want to quickly remind that conversion from percentage to decimal requires moving the decimal point two places to the left (5% = .05, 15% = .15, 12% = .12)

The first step to solving this problem is defining the variables.  For this problem:

x is the volume of "Gently Green"

y is the volume of "Sun Saver"

If we add the volume of "Gently Green" (x) to the volume of "Sun Saver" (y), we get the total volume (90L)

x + y  = 90

The amount of nitrogen from the "Gently Green" (.05x) added to the amount of nitrogen from "Sun Saver" (.15y) will produce the total amount of nitrogen in the solution (.12 *90)

.05x + .15y = .12*90 or .05x + .15y = 10.8

I am going to use substitution method, but you can solve this by elimination method.

x + y = 90                       Formula 1

x = 90 - y                        Subtract y from each side

.05x + .15y = 10.8            Formula 2

.05(90 - y) + .15y = 10.8  Substitution

4.5 -.05y + .15y = 10.8     Distrubute the .05

4.5 + .1y = 10.8                Simplify (-.05y + .15y = .1y)

.1y = 10.8 - 4.5                Subtract 4.5 from each side

.1y = 6.3                          Simplify (10.8 - 4.5 = 6.3)

y = 6.3(10)                       Multiply both sides by 10

y = 63                              Simplify (6.3 X 10 = 63)

x = 90 - y                         Formula as solved for x in step 2

x = 90 - 63                       Substitution

x = 27                              Simplify (90 - 63 = 27)

Therefore, 27 L of "Gently Green" and 63 L of "Sun Saver" should be used.