Jacod and Zachary go to movie threater and purchase refrements for their friends. Jacod spends a total of $18.25 on two bags of popcorn and three drinks. Zachary spends a total $27.50 for four bags of popcorn and two drinks. What is the cost for purchasing one bag of popcorn and one drinks?

Answer

To solve the problem step by step, we will define variables for the costs of popcorn and drinks, set up equations based on the information given, and then solve those equations.

### Step 1: Define Variables
Let:
- \( X \) = cost of one bag of popcorn (in dollars)
- \( Y \) = cost of one drink (in dollars)

### Step 2: Set Up Equations
From the information provided:
1. Jacod spends $18.25 on 2 bags of popcorn and 3 drinks:
\[ 2X + 3Y = 18.25 \quad \text{(Equation 1)} \]

2. Zachary spends $27.50 on 4 bags of popcorn and 2 drinks:
\[ 4X + 2Y = 27.50 \quad \text{(Equation 2)} \]

### Step 3: Simplify Equation 2
We can simplify Equation 2 by dividing all terms by 2:
\[ 2X + Y = 13.75 \quad \text{(Equation 3)} \]

### Step 4: Solve the System of Equations
Now we have two equations:
1. \( 2X + 3Y = 18.25 \) (Equation 1)
2. \( 2X + Y = 13.75 \) (Equation 3)

To eliminate \( 2X \), we can subtract Equation 3 from Equation 1:
\[ (2X + 3Y) - (2X + Y) = 18.25 - 13.75 \]
This simplifies to:
\[ 2Y = 4.50 \]
Now, divide both sides by 2:
\[ Y = 2.25 \]

### Step 5: Substitute Back to Find X
Now that we have \( Y \), we can substitute it back into Equation 3 to find \( X \):
\[ 2X + 2.25 = 13.75 \]
Subtract 2.25 from both sides:
\[ 2X = 11.50 \]
Now, divide by 2:
\[ X = 5.75 \]

### Step 6: Calculate Total Cost for One Bag of Popcorn and One Drink
Now we can find the total cost for purchasing one bag of popcorn and one drink:
\[ X + Y = 5.75 + 2.25 = 8.00 \]

### Final Answer
The cost for purchasing one bag of popcorn and one drink is **$8.00**.

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