A set theory question which seems to lack some information? This question seems to have a minimum and maximum value solution. It seems that it would not have enough information for an answer. But it has an exact solution.

A box contains 20 black, 15 white and 40 green beads. There are 30 glass beads, and the remainder are made of brass. The number of black brass beads is equal to the number of white glass beads. How many glass beads are green?

I tried to solve this by drawing a Venn Diagram with a universal set of 75 beads, 30 glass beads and 45 brass beads. Then we can have 15 black brass maximum because equal 15 white glass beads. But it can also have 14 black brass and 14 white glass, right? Then how can we know the number of green glass beads for certain?
Any helps are greatly appreciated. Many thanks!
 A: Consider this table:
$$\begin{array}{|r|c|c|c|c|} 
 & \text{Black} & \text{White} & \text{Green} & \text{Total}\\ \hline
\text{Brass} & & & & 45\\ \hline
\text{Glass} & & & & 30 \\ \hline
\text{Total} & 20 & 15 & 40 & 75
 \end{array}$$
Let $x$ be the number of black brass beads (and white glass ones). Then:
$$\begin{array}{|r|c|c|c|c|} 
 & \text{Black} & \text{White} & \text{Green} & \text{Total}\\ \hline
\text{Brass} & x& & & 45\\ \hline
\text{Glass} & & x& & 30 \\ \hline
\text{Total} & 20 & 15 & 40 & 75
 \end{array}$$
So we can complete black and white columns of the table to:
$$\begin{array}{|r|c|c|c|c|} 
 & \text{Black} & \text{White} & \text{Green} & \text{Total}\\ \hline
\text{Brass} & x& 15-x& & 45\\ \hline
\text{Glass} & 20-x& x& & 30 \\ \hline
\text{Total} & 20 & 15 & 40 & 75
 \end{array}$$
Which leads to completing the two rows:
$$\begin{array}{|r|c|c|c|c|} 
 & \text{Black} & \text{White} & \text{Green} & \text{Total}\\ \hline
\text{Brass} & x& 15-x& 30& 45\\ \hline
\text{Glass} & 20-x& x& 10& 30 \\ \hline
\text{Total} & 20 & 15 & 40 & 75
 \end{array}$$
There are $10$ green glass beads.
