Let x and y represent both numbers.
Given:
x = 1/4 * y
x + y = 15
Let's find the two numbers.
We have the system of equations:
[tex]\begin{gathered} x=\frac{1}{4}y \\ \\ x+y=15 \end{gathered}[/tex]Plug in 1/4y for x in the second equation:
[tex]\begin{gathered} \frac{1}{4}y+y=15 \\ \\ \\ \frac{5}{4}y=15 \\ \\ 1.25y=15 \end{gathered}[/tex]Divide both sides by 1.25:
[tex]\begin{gathered} \frac{12.5y}{1.25}=\frac{15}{1.25} \\ \\ y=12 \end{gathered}[/tex]Now, to solve for x plug in 12 for y in either the first or second equation.
Let's take the first equation:
[tex]\begin{gathered} x=\frac{1}{4}y \\ \\ x=\frac{1}{4}*12 \\ \\ x=3 \end{gathered}[/tex]Therefore, the numbers are:
3, 12
ANSWER:
3, 12
