Orange juice, a raisin bagel, and a cup of coffee from Billy's Breakfast Bar cost a total of $\$ 2.65$. Billy posts a notice announcing that, effective the following week, the price of orange juice will increase $50 \%$ and the price of bagels will increase $20 \%$. After the increase, the same purchase will cost a total of $\$ 3.30$, 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? \$
Answer
Final Answer: The cost of a glass of orange juice before the increase was \(\boxed{0.80}\), the cost of a raisin bagel before the increase was \(\boxed{1.25}\), and the cost of a cup of coffee before the increase was \(\boxed{0.60}\).
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 \(\boxed{0.80}\), the cost of a raisin bagel before the increase was \(\boxed{1.25}\), and the cost of a cup of coffee before the increase was \(\boxed{0.60}\).
