John and his children went into a movie theater and he bought $44.25 worth of drinks and pretzels. Each drink costs $5 and each pretzel costs $4.75. He bought twice as many drinks as pretzels. Determine the number of drinks and the number of pretzels that John bought.

To solve this problem, we need to set up a system of equations based on the given information.

Let's denote:
- $ x $ as the number of pretzels John bought.
- $ y $ as the number of drinks John bought.

We are given two key pieces of information:
1. The total cost of drinks and pretzels is $44.25.
   \[
   4.75x + 5y = 44.25
   \]
2. John bought twice as many drinks as pretzels.
   \[
   y = 2x
   \]

### Step 1: Substitute $ y = 2x $ into the first equation.
We substitute $ y = 2x $ into the equation $ 4.75x + 5y = 44.25 $ to get:
\[
4.75x + 5(2x) = 44.25
\]
Simplify the equation:
\[
4.75x + 10x = 44.25
\]
Combine like terms:
\[
14.75x = 44.25
\]

### Step 2: Solve for $ x $.
\[
x = \frac{44.25}{14.75} = 3
\]

So, $ x = 3 $ pretzels were bought.

### Step 3: Find $ y $ using $ y = 2x $.
Substitute $ x = 3 $ into $ y = 2x $:
\[
y = 2(3) = 6
\]

So, $ y = 6 $ drinks were bought.

### Final Answer:
- **3 pretzels** were bought.
- **6 drinks** were bought.

Would you like further details or have any questions about this solution?

Here are 5 related questions you might find useful:
1. If each pretzel had cost $5 instead of $4.75, how much would the total cost have been?
2. What if John bought three times as many drinks as pretzels—how many of each would he have bought?
3. If John had $50, how many more drinks or pretzels could he have bought with the remaining money?
4. What would the total cost have been if the price of drinks had increased to $6 each?
5. How would the solution change if John had bought equal numbers of drinks and pretzels?

**Tip:** When working with word problems, always translate the given information into equations carefully, ensuring that each condition is represented correctly.

Learn how to solve a word problem involving John's spending on drinks and pretzels at a movie theater. Understand how to set up and solve systems of equations to determine the number of drinks and pretzels bought. Suitable for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation