Orange juice, a raisin bagel, and a cup of coffee from Billy's Breakfast Bar cost a total of $\mathrm{\$}2.65$. Billy posts a notice announcing that, effective the following week, the price of orange juice will increase $50\mathrm{\%}$ and the price of bagels will increase $20\mathrm{\%}$. After the increase, the same purchase will cost a total of $\mathrm{\$}3.30$, and the orange juice will cost twice as much as coffee. Find the price of each item before the increase.
What was the cost of a glass of orange juice before the increase? $
What was the cost of a raisin bagel before the increase? $
What was the cost of a cup of coffee before the increase? $

Step 1 ：Let's denote the cost of orange juice, a raisin bagel, and a cup of coffee before the increase as O, B, and C respectively.

Step 2 ：We know that the total cost before the increase is $O+B+C=2.65$.

Step 3 ：After the increase, the total cost is $1.5O+1.2B+C=3.3$.

Step 4 ：We also know that the cost of orange juice after the increase is twice the cost of coffee, so $1.5O=2C$.

Step 5 ：Solving this system of equations, we find that $B=1.25$, $C=0.60$, and $O=0.80$.

Step 6 ：Final Answer: The cost of a glass of orange juice before the increase was $\boxed{{\displaystyle 0.80}}$, the cost of a raisin bagel before the increase was $\boxed{{\displaystyle 1.25}}$, and the cost of a cup of coffee before the increase was $\boxed{{\displaystyle 0.60}}$.