Assumption and simple calculation

Question

I'm having an issue with what seems to be an simple question. Here it is:

Two hockey teams, team A and team B played a game, Team A beat Team B by 2 goals. The crowd was pleased as there were 8 goals in total for the whole game.

What was the game's scored?

How many goals did team A score and how many did Team B?

My first thought was that because the total goals in the game were 8 and team A won by 2 goals they must had 6 goals and team B had 2 because if team B had scored those 2 last goals they would have a tie. But I'm still confused is my assumptions are right. Any ideas?

Answer 1

Call $x$ the number of the team A goals. Then B made $x-2$ goals. The total goals are $x+(x-2)=8$ then $x=5$

Answer 2

Set up.
$(1)$ $A-B=2$
$(2)$ $A+B=8$
Solve.

Answer 3

If I may, how did you deduce that Team A scored 6 goals and team B scored 2. There were 8 goals TOTAL for the entire game. And we know the condition $$Ascore= Bscore+2$$ Knowing that, recall what the total score was and deduce your answer by system of equations.

Answer 4

The answer is $5:3$,

Let's denote $A'$ be the number of goals of team $A$,

and let $B'$ be the number of goals of team $B$

Team $A$ beat Team $B$ by $2$ goals: so $A'=B'+2$ and we also know that $A'+B'=8$

So have two equations with two variables:

$$\begin{cases} A'=B'+2\\ A'+B'=8 \end{cases}$$

So from the first row we get $A'=B'+2$, let set that in the second row we get

$B'+2+B'=8$ so $B'=3$ and $A'=5$