Question

Lindsey Wilson was the top scorer in a women's professional basketball league for the 2006 regular season, with a total of 814 points. The number of two-point field
goals that Lindsey made was 49 less than double the number of three-point field goals she made. The number of free throws (each worth one point) she made was

38 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 Lindsey Wilson made during

the 2006 regular season.

Lindsey Wilson made free throws.

Answer 1

Answer:

The number of free throws, two-point throw, and three-point throw are 135, 173, and 111 respectively.

Step-by-step explanation:

Let x,y, and z are the numbers of two-point field goals, numbers of three-point field goals, and the number of free-throws (one-point goal) respectively.

The total points= 814

$\Rightarrow 2x+3y+z=814\;\cdots(i)$

As the number of two-point  goals was 49 less than double the number of three-point field goals she made.

$\Rightarrow x=2y-49 \;\cdots(ii)$

Again, the number of free goals was 38 less than the number of two-point field goals she made.

$\Rightarrow z=x-38\;\cdots(iii)$

From equations (i) and (iii)

2x+3y+x-38=814

$\Rightarrow 3x+3y=852$

$\Rightarrow x+y=284$

$\Rightarrow 2y-49+y=284$ [using equation (ii)]

$\Rightarrow 3y=333$

$\Rightarrow y=111$

From equation (ii),

$x= 2\times111-38=173$

From equation (iii),

$z=173-38=135$.

Hence,

The number of free throws, z= 135

The number of two-point throw, x=173

The number of three-point throw, y=111.