Question

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 1

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:

$x + y + z = 362$

She scored 636 points, hence:

$x + 2y + 3z = 636$

• 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:

$y = x + 27$

Then:

$x + y + z = 362$

$x + x + 27 + z = 362$

$2x + z = 335$

$z = 335 - 2x$

$x + 2y + 3z = 636$

$x + 2(x + 27) + 3z = 634$

$3x + 3z = 582$

$x + z = 194$

$z = 194 - x$

Equaling both equations for z, finding x:

$335 - 2x = 194 - x$

$x = 141$

Then, to find y and z:

$y = x + 27 = 141 + 27 = 168$

$z = 194 - x = 194 - 141 = 53$

She made:

• 141 free throws.

• 168 two-point field goals.

• 53 three-point field goals.

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