SOLUTION: Team scored 78 points 19 of the baskets counted one point each the remaining 27 were two points in three point shots how many of each kind of shot did the team make

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Question 1047160: Team scored 78 points 19 of the baskets counted one point each the remaining 27 were two points in three point shots how many of each kind of shot did the team make
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
19= number of 1-point baskets/shots
x= number of 2-point baskets/shots
y= number of 3-point baskets/shots
19%2B2x%2B3y= total number of points scored.
"Team scored 78" translates as
19%2B2x%2B3y=78
We translate "the remaining 27 were two points or three point shots" as
x%2By=27 .
We have a system of two equations: system%2819%2B2x%2B3y=78%2Cx%2By=27%29 .
You could easily solve x%2By=27 for x :
x%2By=27 ---> x=27-y ,
and then substitute 27-y for x in the other equation to get
19%2B2%2827-y%29%2B3y=78
19%2B54-2y%2B3y=78
73%2By=78
y=78-73
highlight%28y=5%29 .
Then, substituting 5 for y in x=27-y , you get
x=27-5
highlight%28x=22%29 .

NOTE:
If you have not studied systems of equations,
you could start with
19= number of 1-point baskets/shots
y= number of 3-point baskets/shots,
and since "the remaining 27 were two points or three point shots"
27-y= number of 3-point baskets/shots
"Team scored 78" then translates as
19%2B2%2827-y%29%2B3y=78 ,
and that equation can be solved for y as shown above.

OTHER WAYS: There are other ways to solve the system of equations,
but the result is the same:
there were highlight%285%29 3-point shots,
and highlight%2822%29 2-point shots.