If Sue buys three packets of chips and two bottles of cola, it will cost her $13.20. However, if she buys two packets of chips and three bottles of cola it will cost her only $11.80. What is the price of each item?
90

Let's solve this problem by setting up a system of linear equations based on the information provided.

Let:
- $ x $ be the price of one packet of chips.
- $ y $ be the price of one bottle of cola.

From the problem, we can create the following equations:

1. $ 3x + 2y = 13.20 $  $\quad \text{(Equation 1)}$
2. $ 2x + 3y = 11.80 $  $\quad \text{(Equation 2)}$

### Solving the System of Equations

We can use the method of elimination or substitution to solve for $ x $ and $ y $.

#### Step 1: Multiply both equations to eliminate one variable.
Let's eliminate $ x $. Multiply Equation 1 by 2 and Equation 2 by 3:

- $ 6x + 4y = 26.40 $  $\quad \text{(Equation 3)}$
- $ 6x + 9y = 35.40 $  $\quad \text{(Equation 4)}$

#### Step 2: Subtract Equation 3 from Equation 4 to eliminate $ x $:
\[
(6x + 9y) - (6x + 4y) = 35.40 - 26.40
\]
\[
5y = 9.00
\]

#### Step 3: Solve for $ y $:
\[
y = \frac{9.00}{5} = 1.80
\]

So, the price of one bottle of cola $ y $ is $1.80.

#### Step 4: Substitute $ y = 1.80 $ back into Equation 1 to solve for $ x $:
\[
3x + 2(1.80) = 13.20
\]
\[
3x + 3.60 = 13.20
\]
\[
3x = 13.20 - 3.60 = 9.60
\]
\[
x = \frac{9.60}{3} = 3.20
\]

So, the price of one packet of chips $ x $ is $3.20.

### Final Answer:
- The price of one packet of chips is **$3.20**.
- The price of one bottle of cola is **$1.80**.

Would you like more details on this solution, or do you have any questions?

Here are 8 related questions to consider:
1. What if Sue buys 5 packets of chips and 4 bottles of cola? How much will it cost?
2. How would the solution change if the prices were different?
3. Can you solve a similar problem with different coefficients?
4. How would you check if the solution is correct?
5. What is the graphical representation of the system of equations?
6. Can this problem be solved using matrix methods?
7. What are other methods to solve a system of linear equations?
8. How would you interpret the solution in terms of real-life scenarios?

**Tip:** When solving systems of equations, always check your solution by substituting the values back into the original equations to ensure they satisfy both equations.

Learn how to solve a system of linear equations involving the costs of chips and cola. Understand the step-by-step process to find the prices of chips and cola using mathematical methods. Suitable for students in Grades 7-9.

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