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 n

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.

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Ngọc Diệp 1 month 2021-08-13T19:55:03+00:00 1 Answers 1 views 0

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    2021-08-13T19:56:23+00:00

    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.

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