Question

In a certain dart game, points are awarded for hitting a certain sections of the board. You get 5 points for each hit and lose 3 points for each miss. Each game consists of throwing 10 darts. If one team scores 18 points, how many darts hit the target and how many miss the target?

Use substitution or elimination to solve:

t= dart that hit the target
m= darts that miss the target

t+m=10
5t+3m=18

Answer 1

Well look at that! The equations are already set up.

Let t= dart that hit the target
Let m= darts that miss the target

t+m=10 This equation is true because you throw 10 darts in one game.
5t+3m=18 This equation is true because the team got 18 points.

Now let's use substitution by solving one variable and substituting what the variable equals into the other equation.
t+m=10
m = 10-t
Now substitute 10-t as "m" in the other equation.
5t + 3(10-t) = 18
5t + 30 -3t = 18
2t = -12
t = -6

Now substitute -6 into the equation m=10-t
m = 10 - (-6)
m = 10 + 6
m = 16

Answer 2

so we have
h=hits
m=miss
h+m=10

gain 5 for every hit and lose 3 for every miss
so 5 times number of hit=points from hit
-3 times number of miss=points deducted from miss
add
5h-3m=18
so we have the equations

h+m=10
5h-3m=18

multiply first equation by 3
3h+3m=30
add to first equatio

3h+3m=30
5h-3m=18 +
8h+0m=48


8h=48
divide by 8
h=6
subsitute
h+m=10
6+m=10
subtract 6
m=4


6 hits
4 miss