Question

Hockey teams’ receive 2 points when they win and 1 point when they tie. One season, a team won a championship with 56 points. They won 10 more games than they tied. How many wins and how many ties did the team have?

Answer 1

`22` wins; `12` ties

Explanation:

Let `w` be the number of games won
and `t` be the number of games tied.

We are told:
[1]`color(white)("XXX")2w+1t=56`
[2]`color(white)("XXX")w=t+10`

Using [2] substitute `(t+10)` for `w` in [1]
[3]`color(white)("XXX")2(t+10)+t=56`

Simplifying
[4]`color(white)("XXX")3t+20=56`

[5]`color(white)("XXX")3t=36`

[6]`color(white)("XXX")t=12`

Using [6] substitute `12` for `t` in [2]
[7]`color(white)("XXX")w=12+10`

[8]`color(white)("XXX")w=22`