SOLUTION: A midwestern music competition awarded 43 ribbons. The number of blue ribbons awarded was 2 less than the number of white ribbons. The number of red ribbons was 3 more than the num

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Question 1149085: A midwestern music competition awarded 43 ribbons. The number of blue ribbons awarded was 2 less than the number of white ribbons. The number of red ribbons was 3 more than the number of white ribbons. How many of each kind of ribbon was awarded.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
b, Blue ribbons
w, White ribbons
r, Red ribbons



More than one way to solve.
Maybe try rewriting first equation all in terms of one variable, using the second and third equations...





-------------------and maybe you can finish from here.


Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.

Let x be the number of white ribbons.


Then the number of blue ribbon was  (x-2),  while the number of red ribbons was (x+3).


The total number equation


    x + (x-2) + (x+3) = 43.


Simplify and solve


    3x + 1 = 43

    3x     = 43 - 1 = 42

     x     = 42/3 = 14.


ANSWER.  14 white ribbons,  14-2 = 12 blue ribbons  and 14+3 = 17 red ribbons.


CHECK.  14 + 12 + 17 = 43.    ! Correct !

Solved.


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