Linear equations

Question

Lindsay was the top scorer in a woman’s basketball league for 2006, with a total of 854 points. The number of two point field goals that Lindsay made was 58 less than double the number of three point field goals she made. The number of free throws, each worth one point, she made was 34 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 Lindsay made during the 2006 season.

Answer 1

F= free throws

T= 2 point shots

X=3 point shots

F +2T + 3X = 854

T = 2X -58

F = T - 34

T-34 + 2T + 3x = 854 => 3T + 3x = 888

3(2X - 58) + 3X = 888

9X-174=888

X = 118

substitute back to get T=178 and F = 144

The use these value to substitute in the first equation to make sure the answers are correct.