Andrea Drew was the top scorer in a womans professional bask

Andrea Drew was the top scorer in a woman’s professional basketball league for the 2006 regular season, with a total of 872 points. The number of two-point field goals that Andrea made was 68 less than double the number of three-point field goals she made. The number of free throws (each worth one point) she made was 40 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 Andrea Drew made during the 2006 regular season.

Andrea Drew made 140 free throws.

Andrea Drew made how many two-point field goals.

Andrea Drew made how many three-point field goals.

Solution

Let the number of two-point field goals that Andrea made in the 2006 season be x, the number of three-point field goals she made be y and the number of free throws be z.Then, 2x + 3y + z = 872...(1) ; x = 2y - 68...(2) and z = x - 40...(3).

On substituting z = x - 40 in the first equation, we get 2x + 3y + x - 40 = 872 or, 3x + 3y = 872 + 40 = 912, or, x + y = 1/3(912) or, x + y = 304...(4) Now, on substituting x = 2y - 68 ( from the 2nd equation) in the 4th equation, we get 2y - 68 + y = 304 or, 3y = 304 + 68 = 372 so that y = 1/3(372) = 124. Now, from the 2nd equation, we have x = 2y - 68 = 2*124 - 68 = 248 - 68 = 180. Also, z = x - 40 ( from the 3rd equation) = 180 - 40 = 140. Thus, the number of two-point field goals that Andrea made in the 2006 season is 180, the number of three-point field goals she made is 124 and the number of free throws she made is 140. We can verify the result by substituting these values of x, y, z in any of the equations 1, 2, 3.e.g, on verification, the 1st equation changes to 2*180+3*124 + 140 = 872 or, 360 + 372 + 140 = 872, which is correct. Similarly 140 = 180 - 40 and 180 = 2* 124 - 68.