Question

Rebecca Wilson was the top scorer in a​ women's professional basketball league for the 2006 regular​ season, with a total of 846 points. The number of​ two-point field goals that Rebecca made was 77 less than double the number of​ three-point field goals she made. The number of free throws​ (each worth one​ point) she made was 30 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 Wilson made during the 2006 regular season.

Answer 1

Number of two point goals = 169

Number of three point goals = 123

Number of free throws = 139

Explanation:

Let the number of two point goals =
`x`

Let the number of three point goals =
`y`

Let the number of free throws =
`z`

As per the given statements:

`x = 2y-77 ...... (1)`

`z = x-30 ...... (2)`

Using equation (1):

`z = 2y-107` ...... (3)

Total number of points from two point goals =
`2x`

Total number of points from three point goals =
`3y`

Total number of points from free throws =
`z`

`2x+3y+z=846`

using (1) and (3):

`2(2y-77)+3y+2y-107=846\\\Rightarrow 4y-154+5y-107=846\\\Rightarrow 9y-261=846\\\Rightarrow 9y=846+261\\\Rightarrow 9y=1107\\\Rightarrow y =123`

By (1):

`x = 2* 123-77 =169`

By (3):

`z =2* 123-107 = 139`

So, answers are:

Number of two point goals = 169

Number of three point goals = 123

Number of free throws = 139