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) About Me  (Show Source):
You can put this solution on YOUR website!
b, Blue ribbons
w, White ribbons
r, Red ribbons

system%28b%2Bw%2Br=43%2Cb=w-2%2Cr=w%2B3%29

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

b%2Bw%2Br=43
%28w-2%29%2Bw%2B%28w%2B3%29=43
3w%2B1=43
3w=42
w=14-------------------and maybe you can finish from here.


Answer by ikleyn(52781) About Me  (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.