Question

Rebecca Smith was the top scorer in a​ women's professional basketball league for the 2006 regular​ season, with a total of 863 points. The number of​ two-point field goals that Rebecca made was 80 less than double the number of​ three-point field goals she made. The number of free throws​ (each worth one​ point) she made was 13 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 Rebecca Smith made during the 2006 regular season.

Answer 1

Number of free throws = 155,

Number of two-points field goals= 168

Number of two-points field goals= 124

Explanation:

Let x,y, and z be the numbers of free throws, two-point field goals and three-point field goals she made.

As she scored a total of 863 points, so

x+2y+3z=863...(i)

As the number of​ two-point field goals that Rebecca made was 80 less than double the number of​ three-point field goals she made, so

2z-y=80

Or y=2z-80...(ii)

As the number of free throws​ (each worth one​ point) she made was 13 less than the number of​ two-point field goals she made, so

y-x=13

-x= 13-y

-x= 13-(2z-80)

-x= 93-2z

x=2z-93...(iii)

Now, put the values from equation (ii) and (iii) to equation (i), we have

(2z-93)+2(2z-80)+3z=863

2z-93+4z-160+3z=863

9z=863+93+160=1116

z=1116/9=124

From equation (ii)

y=2x124-80=168

and from equation (iii)

x=2x124-93=155.

Hence, the number of free​ throws, two-point field​ goals, and​ three-point field goals Rebecca Smith made during the 2006 regular season are 155, 168, and 124 respectively.