Three variable linear equations

Question

Chuck was the leading scorer in the 2009 league. Chuck scored a total of 798 points during the 2009 season. He made 45 more one-point free throws than two-point field goals, and his number of two-point field goals was 9 less than 25 times his number of three-point field goals. How many free throws, two-point field goals, and three-point field goals did chuck make in 2009?

Answer 1

Let

x = number of free throws (1 point)

y = number of field goals (2 points)

z = number of three-pointers (3 points)

 

The first equation we can make is 798 = x + 2y + 3z for the total number of points. We can also make x = 45 + y and y = 25z - 9 for the other two statements. These three equations are enough to completely solve the system:

 

798 = (45 + y) + 2y + 3((y + 9) / 25)

 

798 = 45 + 3y + (3 / 25)y + (27 / 25)

 

Multiply both sides by 25

 

19950 = 1125 + 75y + 3y + 27

 

18798 = 78y

 

y = 241

 

x = 45 + 241

 

x = 286

 

z = (y + 9) / 25

 

z = (241 + 9) / 25 = 250 / 25

 

z = 10

 

Double check:

 

798 = 286 + 2(241) + 3(10)

 

798 = 286 + 482 + 30

 

798 = 798