A midwestern music competition awarded 40 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 white ribbons. How many of each kind of ribbons was awarded?
white ribbons --- x
blues ---------- x-2
reds ----------- x+3
form the equation and continue
To find the number of each kind of ribbons awarded, we can set up a system of equations.
Let's use the variables B, W, and R to represent the number of blue, white, and red ribbons, respectively.
From the given information, we know the following:
1) The total number of ribbons awarded is 40:
B + W + R = 40
2) The number of blue ribbons is 2 less than the number of white ribbons:
B = W - 2
3) The number of red ribbons is 3 more than the number of white ribbons:
R = W + 3
Now we can solve the system of equations:
Substitute equation 2) and equation 3) into equation 1) to eliminate B and R:
(W - 2) + W + (W + 3) = 40
3W + 1 = 40
3W = 40 - 1
3W = 39
W = 39/3
W = 13
Now we know that W = 13. Substitute this value into equations 2) and 3) to find the values of B and R:
B = W - 2
B = 13 - 2
B = 11
R = W + 3
R = 13 + 3
R = 16
So, there were 11 blue ribbons, 13 white ribbons, and 16 red ribbons awarded in the competition.