a Midwestern music competition awarded 28 ribbons. The number of blue ribbons awarded was 1 less then the number of white ribbons. The number of red ribbons was 2 more then the number of white ribbons. How many of each kind of ribbons was awarded?
w - 1 = b
r = w + 2
r + w + b = 28
(w+2)+ w + (w-1) = 28
Solve for w, then r and b.
Two minor league baseball players got a total of 356
hits. Washington had 20
more hits than Sanchez. Find the number of hits for each player.
To solve this problem, let's define some variables:
Let's say the number of white ribbons awarded is 'x'.
Then, the number of blue ribbons awarded would be 'x - 1' since it is 1 less than the number of white ribbons.
The number of red ribbons awarded would be 'x + 2' since it is 2 more than the number of white ribbons.
According to the problem, the total number of ribbons awarded is 28. So, we can set up an equation based on this:
x + (x - 1) + (x + 2) = 28
Now, let's solve this equation to find the value of 'x' and hence determine the number of each type of ribbons awarded.
x + x - 1 + x + 2 = 28
3x + 1 = 28
3x = 27
x = 9
Now that we have the value of 'x', we can substitute it into our expressions for the number of each type of ribbon:
Number of white ribbons = x = 9
Number of blue ribbons = x - 1 = 9 - 1 = 8
Number of red ribbons = x + 2 = 9 + 2 = 11
Therefore, there were 9 white ribbons, 8 blue ribbons, and 11 red ribbons awarded in the competition.