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
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
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. <span>5t+3m=18 This equation is true because the team got 18 points. </span> 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
Based on the information given in the question, the inequality which can be used to determine x, the number of people who can go to the amusement park will be:
8 + 23(x) ≤ 100
8 + 23x ≤ 100
23x ≤ 100 - 8
23x ≤ 92
x ≤ 92/23
x ≤ 4
The number of people that can go to the amusement park will be at most 4