can anyone please show me how to set this up?
This basketball season, Armando scored 8 less points than Austin, Damien scored twice as many points as Austin, and Brian scored 5 more than 5 times as many points as Austin. If all 4 players scored a total of 267 points this season, how man points did each player score?
Ar + Au + D + B = 267
Ar = Au - 8
D = 2 Au
B = 5 Au + 5
substitute in the 1st equation to find Au
... then substitute back to find the others
Thanks scott!
To solve this problem, we need to set up and solve a system of equations. Let's assign variables to each player's score:
Let Austin's score be A.
Armando's score will be A - 8 (since he scored 8 less points than Austin).
Damien's score will be 2A (since he scored twice as many points as Austin).
Brian's score will be 5A + 5 (since he scored 5 more than 5 times as many points as Austin).
Now we can set up the equation to represent the total score of all four players:
A + (A - 8) + 2A + (5A + 5) = 267
Let's simplify this equation:
A + A - 8 + 2A + 5A + 5 = 267
9A - 3 = 267
Now, we can solve for A:
9A = 267 + 3
9A = 270
A = 270 / 9
A = 30
So, Austin scored 30 points.
Now we can substitute this value back into the other equations to find the scores of the other players:
Armando's score = A - 8 = 30 - 8 = 22
Damien's score = 2A = 2(30) = 60
Brian's score = 5A + 5 = 5(30) + 5 = 155
Therefore, Austin scored 30 points, Armando scored 22 points, Damien scored 60 points, and Brian scored 155 points.