Erin competes in track meets. She has won blue ribbons and red ribbons. For every 3 blue ribbons she has won, she has won 2 red ribbons.

Question

At the end of the track season, Erin has won 30 ribbons in total.
Use the drop-down menus to complete the statement about the number of blue ribbons and the number of red ribbons Erin has won.
Erin has won
(Select)
blue ribbons and
(Select)
red ribbons.

Answer 1

Let the number of blue ribbons Erin has won be represented by \( b \) and the number of red ribbons be represented by \( r \). According to the problem, the relationship between blue and red ribbons is given by:

\[ \frac{b}{r} = \frac{3}{2} \]

This can be rewritten as:

\[ 2b = 3r \]

It's also given that the total number of ribbons won by Erin is:

\[ b + r = 30 \]

Now, we can express \( r \) in terms of \( b \):

\[ r = 30 - b \]

Substituting this expression for \( r \) into the equation \( 2b = 3r \):

\[ 2b = 3(30 - b) \]

Expanding this yields:

\[ 2b = 90 - 3b \]

Adding \( 3b \) to both sides results in:

\[ 5b = 90 \]

Now, divide by 5:

\[ b = 18 \]

Now we can find \( r \):

\[ r = 30 - b = 30 - 18 = 12 \]

So, Erin has won 18 blue ribbons and 12 red ribbons.

To complete the statement:

Erin has won 18 blue ribbons and 12 red ribbons.