Given:
A number is 11, more than three times another number.
Let, larger number be x, and the smaller be y.
[tex]x=11+3y\ldots\ldots\text{.}(1)[/tex]The sum of two numbers is 4
[tex]x+y=4\ldots\ldots\text{.}(2)[/tex]Solve the two equations,
[tex]\begin{gathered} \text{Put the values of x from equation (1) in (2)} \\ x+y=4 \\ 11+3y+y=4 \\ 11+4y=4 \\ 4y=4-11 \\ 4y=-7 \\ y=-\frac{7}{4} \end{gathered}[/tex]Now,
[tex]\begin{gathered} x=11+3y \\ x=11+3(-\frac{7}{4}) \\ x=11-\frac{21}{4} \\ x=\frac{23}{4} \end{gathered}[/tex]Answer: The larger number is x=23/4.
