John R. answered • 12/22/12

John R: Math, Science, and History Teacher

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.