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:
[tex]x+y=5.25[/tex]
The sum of 0.40x and 0.25y has to be 0.30*5.25, this is:
[tex]\begin{gathered} 0.40x+0.25y=0.30\cdot5.25 \\ 0.40x+0.25y=1.575 \end{gathered}[/tex]
Solve the system of equations, use substitution to do it:
[tex]\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=\frac{0.2625}{0.15} \\ x=1.75=1\frac{3}{4} \end{gathered}[/tex]
Use the value of x to find y:
[tex]\begin{gathered} y=5.25-x \\ y=5.25-1.75 \\ y=3.5=3\frac{1}{2} \end{gathered}[/tex]
It means that the answer is the first choice 1 3/4 gallons of 40% gloss and 3 1/2 gallons of 25% gloss.
