Question

Hockey teams receive 2 points when they win and 1 point when they tie. One season, a team won a championship with 48 points. They won 9 more games than they tied. How many wins and ties did they have?

Answer 1

you need to get two equations out of this question to solve

Answer 2

we have two key pieces of information that tell us what these two equation will look like: they recieved 48 points at the end of the season, they won 9 more games than they tied

Answer 3

let us use the variables W for win and T for tie

Answer 4

our first equation will be derrived from the 48 points piece of data. since wins are worth 2 points and ties are worth 1, our first equation will be

2*W+T=48

Answer 5

next, we know that they won 9 more games than they tied, so we also know

W=T+9
or, to make it easier to plug in,

T=W-9

Answer 6

if you plug this second equation into the first one, what do you get?

Answer 7

?

Answer 8

we have two equations,

1) 2W+T=48

2) T=W-9

we are going to substitute the second equation into the first for T

Answer 9

look at it like this

2*W+(T)=48

Answer 10

now substituting

2W+(W-9)=48

Answer 11

all i did was replace T with (W-9)

Answer 12

now we remove the brackets

2W+W-9=48

Answer 13

combine the W terms

3W-9=48

Answer 14

add 9 to both sides

3W=57

Answer 15

and divide by 3

W=19

Answer 16

voila, we now know how many games they won in the season, 19

Answer 17

now, remembering the identity we used for T

T=W-9

substitute this value in for W

Answer 18

10

Answer 19

you got it

Answer 20

for any problem like this, you will have these same steps to follow

Answer 21

1) get two equations

2) use one of these equations to get an identity for one variable in terms of the other

3) substitute the identity into the the other equation

4) solve

thats all there is to it