System of Equations word problem I can't figure out!!!!

Question

A basketball player scored 40 points in a game. The number of three-point field goals the player made was 22 less than three times the number of free throws (each worth 1 point). Twice the number of two point field goals the player made was 11 more than the number of three point field goals made. Find the number of free-throws, two point field goals, and three point field goals that the player made in the game.

Once I have the equations I understand how to do the problem, but I am obviously doing something wrong because each time I write out the equations I end up getting fractions. 

Answer 1

If you let x represent the number of free throws (worth 1 point each)

          let y represent the number of two-point field goals (worth 2 points each)

          let z represent the number of three-point shots made (worth 3 points each)

 

Then the correct system of linear equations is as follows:

 

x + 2y + 3z = 40         (The total number of points scored is 40.)

z = 3x - 22                  (The number of 3-pointers was 22 less than 3 times the number of free throws.)

2y = z + 11                 (Twice the number of 2-point shots made was 11 more than the number of 3-pointers.) 

 

The solution is as follows:

 

This basketball player scored 9 points via free throws (9 at 1 point each), 16 points via 8 two-point shots made, and 15 points via 5 three-point shots made.

 

One should then re=read each statement presented in the paragraph to be sure that these numbers make a true statement out of every one of the sentences in this paragraph. I checked them and they do ! My method to solve this was to utilize row-reduced echelon form, a technique a learned in college about 40 years ago. (After i dusted it off, of course.)

 

Answer 2

Try:

 

x = one pointer

y = two pointer

z= three pointer

 

x + y + z + 40

z = 3x - 22

2y = z + 14