Systems of Equations

Question

While playing for the LA lakers, Vlade Divac scored 25 points in a game against the Bulls. In basketball it is possible to score a 3 point field goal, 2 point field goal and a 1 point free throw/ He made as many free throws as three pointers and two pointers combine. He scored one point less with three pointers than he did with pointers and free throws combine. How many of each shot did he make?

Answer 1

First choose names for the different shots...

For example, FG is the number of 3 pointers, fg is the number of 2 pointers, ft is the number of free throws - 1 pointers.

 

The number of points scored in 3-pointers is 3 *FG...  and so on.

 

Total points scored is 3FG + 3fg + 1ft.  (What does that equal?)

 

He made as many free throws as 3-pointers and 2-pointers combined is written ft = FG + fg.

 

The points scored is written 2fg + 1ft = 3FG -1.

 

Now you have 3 equations and 3 unknowns.  Be sure you put all the variables in each equation in the same order!