Algebra help needed

Question

Emily was the top scorer in a​ women's professional basketball league for the 2006 regular​ season, with a total of 822 points. The number of​ two-point field goals that Emilymade was 55

less than double the number of​ three-point field goals she made. The number of free throws​ (each worth one​ point) she made was 21 less than the number of two-point field goals she made. Find how many free throws, two-point field goals, and three-point field goals Emily made during the 2006 regular season.

Answer 1

Set Number of 2-point goal she made as x, 3-point goal she made as y, 1-point goal she made as z.

Then we can conclude three equations:

1. 2y-x=55
2. x-z=21
3. 2x+3y+z=882

From equation 1 and 2, let them all equal to x, get 2y-55=z+21, get z=2y-76

From equation 1, get x=2y-55

Plug everything into equation 3, get 2(2y-55)+3y+(2y-76)=882, solve y=118.67

Back to equation 1, get x=182.33

Back to equation 2, get z=161.33

I doubt the question might be wrong because number of goals should be integer, correct me if I'm made mistakes, thank you!

Answer 2

2x=2*3y-55............................2pt

1z=(2*3y-55)-21......................1pt

(2*3y-55)*2-21=822 y=3pt

(6y-55)*2-21=822

12y-110-21=822

12y=953

y=79.42

x=210.75

z=531.83