Question

A midwestern music competition awarded 34 ribbons. The number of blue ribbons awarded was 1 less than the number of white ribbons. The numbers of red ribbons was 2 more than the number of white ribbons. How many of each kind of ribbon was awarded?

Answer 1

We know that

The total number of ribbons is 34, this can be expressed as x + y +z = 34. Where y represents blue ribbons and x represents white ribbons, and z represents red ribbons.

The blue ribbons awarded was 1 less than the number of white ribbons. This can be expressed as y = x - 1.

The number of red ribbons was 2 more than the number of white ribbons, this can be expressed as z = x + 2.

First, we combine the second and third equations with the first one.

`x+x-1+x+2=34`

Then, we solve for x

`\begin{gathered} 3x+1=34 \\ 3x=34-1 \\ 3x=33 \\ x=(33)/(3) \\ x=11 \end{gathered}`

There are 11 white ribbons.

Then, we find y and z.

`\begin{gathered} y=11-1=10 \\ z=11+2=13 \end{gathered}`

There are 10 blue ribbons and 13 red ribbons.