Sarah Wilson was the top scorer in a women's professional basketball league for the 2006 regular season, with a total of 861 points. The number of two-point field goals that Sarah made was 65 less than double the number of three-point field goals she made. The number of free throws (each worth one point) she made was
33 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 Sarah Wilson made during
the 2006 regular season

9514 1404 393

Step-by-step explanation:

Let a, b, c represent the number of 1-point, 2-point, and 3-point goals, respectively.

  a +2b +3c = 861 . . . . . . total number of points

  b = 2c -65

  a = b -33

Substituting for a, then b, we have ...

  (b -33) +2b +3c = 861

  3b +3c = 894 . . . . . . . . . . add 33, collect terms

  b +c = 298 . . . . . . . . . . . . divide by 3

  (2c -65) +c = 298 . . . . . . substitute for b

  3c = 363 . . . . . . . . . . . . . add 65

  c = 121 . . . . . . . . . . . . . . . divide by 3

  b = 2(121) -65 = 177

  a = 177 -33 = 144

Sarah Wilson made ...