In a recent season, Monique Currie of the Duke Blue Devils scored 635 points. She made a total of 356 shots, including 3 point field goals, 2-point field goals, and 1-point free throws. She made 76 more 2-point field goals than free throws and 77 more free throws than 3-point field goals. Find the number of each type of shot she made.
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Let the number of 3pt shots = x
then the number of points gained for x number of shots becomes 3*x=3x
number of free throws is 77 more than 3pt shots i.e. x+77
then the number of points gained for x+77 shots is =1(x+77) =x+77
number of 2pts shots is 76 more than number of free shots i.e. (x+77) +76= x+153
then the number of points gained for x=153 shots is= 2(x+153) = 2x + 306
as per given question, in total she scored 635 points
3x + (x+77) + (2x+306) = 635
opening the brackets, it becomes
3x + x + 77 + 2x + 306 = 635
6x + 383 = 635
6x= 635 - 383
6x = 252
x = 252 / 6
x = 42
now, number of 3 pt shots = x = 42
number of free throws = x+77 = 42 + 77 = 119
Number of 2 pt shots = x + 153 = 195
Total number of shots is 356
no. of 3 pt shots is 42
number of free throws is 119
number of 2pt shots is 195
as per question
42 + 119 + 195 = 356