how to solve this ?

Question

a basketball player scored 35 times during one game. he scored a total of 56 points, two for each field goal and one for each free throw. how many field did he make? how many free throws? 

Answer 1

Hi Ifran,

 

Let's begin by assigning letters to represent the two unknowns:

    G = number of field goals

    T = number of free throws

 

Now we'll write two equations using the letters to represent the unknowns based upon the numerical relationships given in the problem:

    Equation #1 (number of times scored):

        G + T = 35

    Equation #2 (number of points scored):

        2G + T = 56 (2 pts. per FG; 1 pt. per FT)

 

If we look at our two equations, we can see that if we subtract Equation #1 from Equation #2, we can eliminate T (number of free throws) and get the answer for G (number of field goals):

    2G + T = 56

 - ( G + T = 35)

     ------------------

      G       = 21 (number of field goals)

 

Now we can plug in the value for G (number of field goals) into Equation #1 and get the value for T (number of free throws):

    G + T = 35

   21 + T = 35

           T = 35 - 21

           T = 14 (number of free throws)

 

General procedure for solving word problems:

    1.  Represent unknown(s) with letter(s).

    2.  Write equations using letter(s) for unknown(s) based upon numerical relationship(s) given in the problem, which can then be used to  solve for the unknown(s).

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.