Question

A paint mixer wants to mix paint that is 40% gloss with paint that is 25% gloss to make 5.25 gallons of paintthat is 30% gloss. How many gallons of each paint shpuld the paint mixer mix together?

Answer 1

To solve this question, we have to state a system of equations using the information given to us.

Let x be the gallons of the first paint and y be the gallons of the second paint.

The sum of x and y has to be 5.25, it means:

`x+y=5.25`

The sum of 0.40x and 0.25y has to be 0.30*5.25, this is:

`\begin{gathered} 0.40x+0.25y=0.30\cdot5.25 \\ 0.40x+0.25y=1.575 \end{gathered}`

Solve the system of equations, use substitution to do it:

`\begin{gathered} y=5.25-x \\ 0.40x+0.25(5.25-x)=1.575 \\ 0.40x+1.3125-0.25x=1.575 \\ 0.40x-0.25x=1.575-1.3125 \\ 0.15x=0.2625 \\ x=(0.2625)/(0.15) \\ x=1.75=1(3)/(4) \end{gathered}`

Use the value of x to find y:

`\begin{gathered} y=5.25-x \\ y=5.25-1.75 \\ y=3.5=3(1)/(2) \end{gathered}`

It means that the answer is the first choice 1 3/4 gallons of 40% gloss and 3 1/2 gallons of 25% gloss.