SOLUTION: Anna scored 646 points making 355 shots, including 3-point field goals, 2-point field goals, and 1-point free throws. She made 27 more 2-point field goals than 3-point field goals.

Question 1012706: Anna scored 646 points making 355 shots, including 3-point field goals, 2-point field goals, and 1-point free throws. She made 27 more 2-point field goals than 3-point field goals. Write a system of three equations that represents the number of goals Anna made
Find the number of each type of goal she made for
3-point goals
2-point goals
1-point free throws
Found 2 solutions by Boreal, josmiceli:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
x=FT
y=2point
z=3 point
x+y+z=355
y-27=z
x+2y+3z=646
=========
x+y+y-27=355;;;x+2y+3(y-27)=646;;;x+2y+3y-81=646
x+2y-27=355
x+2y=382
x+5y=727
-3y=-345
y=115
x+575=727
x=152
z=88
(152,115,88)=355 shots
152+230+264=646 points

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let =number of 1-point shots
Let =number of 2-point shots
Let =number of 3-point shots
---------------------------------
(1)
(2)
(3)
-----------------------
This is 3 equations and 3 unknowns,
so it is solvable
-------------------
Substitute (3) into (2)
(2)
(2)
(2)
---------------------
Substitute (3) into (1)
(1)
(1)
----------------------
Subtract (1) from (2)
(2)
(1)
--------------------

and
(3)
(3)
(3)
and
(1)
(1)
(1)
(1)
-----------------
88 3-point goals
115 2-point goals
152 1-point free throws
-----------------------
check:
(2)
(2)
(2)
(2)
You can check other 2 equations
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