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dem82 [27]
2 years ago
13

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.
Mathematics
1 answer:
RUDIKE [14]2 years ago
3 0

Answer:

Number of two point goals = 169

Number of three point goals = 123

Number of free throws = 139

Step-by-step 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\times 123-77 =169

By (3):

z =2\times 123-107 = 139

So, answers are:

Number of two point goals = 169

Number of three point goals = 123

Number of free throws = 139

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