a midwestern music competition awarded 32 ribbons. the number of blue ribbons awarded was 3 less than the number of white ribbons. the number of red ribbons was 2 more than the number of white ribbons. how many of each kind of ribbon was awarded?
A midwestern music competition awarded 31 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?
Let white ribbons be k
Blue will be k-3
Red will be k+2
Sum of white, blue and red... 32
Therefore... K +k-3+k+2=32
3k-1=32
3k=32+1
3k=33.... Divide both side with 3
K=11
Blue =8
White =11
Red =13
To determine the number of each kind of ribbon awarded, let's assign variables to represent the unknowns:
Let's say the number of white ribbons is W.
Then the number of blue ribbons is W - 3 (3 less than the number of white ribbons).
And the number of red ribbons is W + 2 (2 more than the number of white ribbons).
Now, let's set up an equation to solve for W. Since the total number of ribbons awarded is 32, we have:
W + (W - 3) + (W + 2) = 32
Simplifying the equation, we get:
3W - 1 = 32
Adding 1 to both sides:
3W = 33
Now, divide both sides by 3:
W = 11
Therefore, there were 11 white ribbons awarded, 11 - 3 = 8 blue ribbons awarded, and 11 + 2 = 13 red ribbons awarded.
make a let statement
letx=white ribbons
letx-3= blue ribbons
letx+2=red ribbons
x+x+2+x-3=32
solve