Using a system of equations, it is found that she made:
- 168 two-point field goals.
- 53 three-point field goals.
For the system, we have that:
- x is the number of free throws made.
- y is the number of two-point field goals made.
- z is the number of three-point field goals made.
She made 362 shots, hence:
[tex]x + y + z = 362[/tex]
She scored 636 points, hence:
[tex]x + 2y + 3z = 636[/tex]
- Observation: I used 636 as there would not be a solution(number of field goals cannot be a fraction) if 634 was used.
She made 27 more 2-point field goals than free throws, hence:
[tex]y = x + 27[/tex]
Then:
[tex]x + y + z = 362[/tex]
[tex]x + x + 27 + z = 362[/tex]
[tex]2x + z = 335[/tex]
[tex]z = 335 - 2x[/tex]
[tex]x + 2y + 3z = 636[/tex]
[tex]x + 2(x + 27) + 3z = 634[/tex]
[tex]3x + 3z = 582[/tex]
[tex]x + z = 194[/tex]
[tex]z = 194 - x[/tex]
Equaling both equations for z, finding x:
[tex]335 - 2x = 194 - x[/tex]
[tex]x = 141[/tex]
Then, to find y and z:
[tex]y = x + 27 = 141 + 27 = 168[/tex]
[tex]z = 194 - x = 194 - 141 = 53[/tex]
She made:
- 168 two-point field goals.
- 53 three-point field goals.
You can learn more about system of equations at https://brainly.com/question/25960609
