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In the 2004 season, Seattle's Lauren Jackson was ranked first in the WNBA for total points and points per game. She scored 634 points making 362 shots, including 3-point field goals, 2-point field goals, and 1-point free throws. She made 27 more 2-point field goals than free throws. Find the number of each type of goal she made.

Answer :

Using a system of equations, it is found that she made:

  • 141 free throws.
  • 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:

  • 141 free throws.
  • 168 two-point field goals.
  • 53 three-point field goals.

You can learn more about system of equations at https://brainly.com/question/25960609

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