Question

There are red and blue marbles in a jar. One-third of the marbles are red. If another marble is added to the jar, then 3/8 of the marbles will be red. How many marbles are blue?

Answer 1

Set up the 2 proportions:

\[\Large \frac{ R }{ N }=\frac{ 1 }{ 3 }\] and \[\Large \frac{ R }{ N+1 }=\frac{ 3 }{ 8 }\]

And then solve the system with substitution.

Answer 2

$$
{r \over r+b}={1 \over3}\\
{r +1\over r+1+b}={3 \over8}\\
3r=r+b \implies r={b\over 2}\\
8(r+1)=3(r+1+b)\implies 5r=-5+3b\\
5\left ({b \over 2 } \right )=-5+3b\\ \implies b=10
$$
That's it!

Let me know if you have any questions.