there are 72 members of the show choir.there are 6 more boys than girls in the choir.write the model of a system for the above situation.

Question

this is algebra, and im working on solving by elimination

Answer 1

 

Let B = number of boys

     G = number of girls

 

Translate:

  "there are 72 members of the show choir"    means B + G = 72      [eq1]

  "there are 6 more boys than girls "    means     B = 6 + G       [eq2]

 

Math:

   B  + G  = 72         [eq1]

   B  -  G  =  6          [from eq2]

 ------------------   [elimination; add equations]

  2B        =  78

    B        =  39        [divide both sides by 2; eq3]

 

    B  +  G  =  72       [eq1]

    B          =   39      [eq3]

 -------------------    [elimination; subtract equations (or multiply by -1, then add)]

            G  =   33

 

There are 39 boys and 33 girls in the show choir.

 

Checking (very important):

  Is   39 + 33 = 72   ?

             72 = 72   ?yes

  Is   39 - 33 = 6   ?

             6 = 6   ?yes

Answer 2

B + G = 72    There are a total of 72 members

B = G + 6      There are 6 more boys than girls

 

Replace B with G+6 in 1st equation to eliminate boys and solve for girls.

 

(G + 6) + G = 72   combine like terms

2G + 6 = 72          subtract 6 from both sides

2G = 66                divide both sides by 2

G = 33

 

B = G+6=33+6 = 39

 

There are 39 boys and 33 girls in the show choir.