GKT101: General Knowledge for Teachers – Math

A light green latex paint that is 20% yellow paint is combined with a darker green latex paint that is 45% yellow paint. How many gallons of each paint must be used to create 15 gallons of a green paint that is 25% yellow paint?

Let $x$ be the number of gallons of the 20% yellow paint and let $y$ be the number of gallons of the 40% yellow paint. This means that we want those two numbers to add up to 15: $x+y=15$.

Now if we want 15 gallons of 25% yellow paint, that means we want $0.25⋅15=3.75$ gallons of pure yellow pigment. The expression $0.20⋅x$ represents the amount of pure yellow pigment in the $x$ gallons of 20% yellow paint. The expression $0.45⋅y$ represents the amount of pure yellow pigment in the $y$ gallons of 45% yellow paint. Combing the last two adds up to the 3.75 gallons of pure pigment in the final mixture:

$0.20x+0.40y=3.75$

The system is: $\left\{\begin{aligned} x+y &=15 \\ 0.20 x+0.45 y &=3.75 \end{aligned}\right.$

We can isolate one variable and use substitution to solve the system:

$x=15−y$

Now solve for $y$.

$\begin{aligned} 0.20(15-y)+0.45 y &=3.75 & & \\ 3-0.20 y+0.45 y &=3.75 & & \text { Distributive Property } \\ 3+0.2 y &=3.75 & & \text { Add like terms. } \\ 0.25 y &=0.75 & & \text { Subtract } 3 . \\ y &=3 & & \text { Divide by } 0.25 \end{aligned}$

Now we can plug in $y=3$ into $x+y=15$:

$x+y=15 \Rightarrow x+3=15 \Rightarrow x=12$

This means 12 gallons of 20% yellow paint should be mixed with 3 gallons of 45% yellow paint in order to get 15 gallons of 25% yellow paint.