there are 43 ribbions. the number of blue ribbions was 2 less than the number of white ribbions. the number of red ribbions was 3 more than the number of white ribbions.how many of each kind of ribbion was awarded
b = the number of blue ribbions
w = the number of blue ribbions
r = the number of red ribbions
b = w - 2
r = w + 3
w + b + r = 43
w + w - 2 + w + 3 = 43
3 w - 2 + 3 = 43
3 w + 1 = 43
3 w = 43 - 1
3 w = 42 Divide both sides by 3
w = 42 / 3
w = 14
b = w - 2 = 14 - 2 = 12
r = w + 3 = 14 + 3 = 17
14 white ribbons
12 blue ribbons
17 red ribbons
w = the number of WHITE ribbions
To solve this problem, let's assign variables to each type of ribbon:
Let's say the number of white ribbons is represented by 'W'.
Let's say the number of blue ribbons is represented by 'B'.
Let's say the number of red ribbons is represented by 'R'.
Based on the given information, we have the following equations:
1) B = W - 2 (the number of blue ribbons was 2 less than the number of white ribbons)
2) R = W + 3 (the number of red ribbons was 3 more than the number of white ribbons)
3) The total number of ribbons is 43: W + B + R = 43
We can use these equations to solve for the values of W, B, and R.
Let's substitute the values of B and R from equations 1 and 2 into equation 3:
W + (W - 2) + (W + 3) = 43
Combine like terms:
3W + 1 = 43
Subtract 1 from both sides:
3W = 42
Divide both sides by 3:
W = 14
Now that we know the value of W, we can substitute it back into equations 1 and 2 to find the values of B and R:
1) B = W - 2
B = 14 - 2
B = 12
2) R = W + 3
R = 14 + 3
R = 17
Therefore, there were 14 white ribbons, 12 blue ribbons, and 17 red ribbons awarded.