Problem solving

Question

A bag is filled with green and blue marbles. There are 35 marbles in the bag. If there are 11 more green marbles than blue marbles, find the number of green marbles and the number of blue marbles in the bag

Answer 1

A "problem-solving" approach:

   For each blue marble, there is a green marble.  Then, there are 11 more green marbles.

   So, 11 green marbles, plus half of what's left (24), which is 12.   23 green marbles.

   And, 12 blue marbles.

 

Check:

    Does  23 + 12 = 35   ?

               35 = 35   ?yes

    Is   23 = 12 + 11   ?

             23 = 23   ?  yes

 

An algebra approach:

     Let    G = number of green marbles

              B = number of blue marbles

"35 marbles in the bag"      means    G + B = 35     [eq1]

"11 more green marbles than blue marbles"   means          G = B + 11     [eq2]

 

Substitution:

    (B + 11) + B = 35                     [use eq2 to substitute for G in eq1]

      2B = 24

        B = 12

Then, use either equation to solve for G.

    G = B + 11

    G = 23

 

Same check.

 

Elimination:

     G    +    B     =  35       [eq1]

     G    -     B     =  11       [from eq2]

 ---------------------------   [elimination; subtract equations]

    2G                 =  24

     G                  = 12    [eq3]

 

     G     +    B     =  35      [eq1]

     G                  =  12      [eq3]

 -------------------------     [elimination; subtract equations]

                   B     =  23

 

Same check.

 

Answer 2

g = b + 11

b + g = 35

 

b + b + 11 = 35

2b = 24

b = 12

 

You got the rest.