Respuesta :
Let us denote the points scored by each of them as follows:
Manuel = M
Skyler = S
Corey = C
Dylan = D
The information in the question can be "translate" into the language of algebra; it's encoding a linear system of equations:
[tex]\begin{cases}M=S-9 \\ D=2S \\ C=5S-2 \\ M+D+C+S=313\end{cases}[/tex]Usually, we use a method for solving this kind of system, but here, there is a trick: Let us add the first three equations up; this gives us
[tex]M+D+C=(S-9)+2S+(5S-2)[/tex]Playing a little with the right-hand side, we get
[tex]M+D+C=8S-11[/tex]Now, let's play a little with the last equation in the system to get
[tex]M+D+C=313-S[/tex]Matching both equations
[tex]8S-11=313-S[/tex]It's an equation with only one variable. We know how to solve it:
[tex]8S+S=313+11[/tex][tex]9S=324[/tex][tex]S=\frac{324}{9}=36[/tex]We've not finished yet. We need to find M, D, and C.
M) Replacing the value S=36 in the first equation, we get
[tex]M=36-9=27[/tex]D) Replacing the value S=36 in the second equation, we get
[tex]D=2(36)=72[/tex]C) Replacing the value S=36 in the third equation, we get
[tex]C=5(36)-2=180-2=178[/tex]