georgina has $8 to spend she discoveers that she can buy either 4 cans of soft drink and 4 chocolate bars or 2 cans of soft drink and 7 chocolate bars how much does each item cost             

Let the cost of a can of soft drink be $ x $ and the cost of a chocolate bar be $ y $.

Based on the information provided, we can set up the following two equations:

1. $ 4x + 4y = 8 $ (from buying 4 cans of soft drink and 4 chocolate bars)
2. $ 2x + 7y = 8 $ (from buying 2 cans of soft drink and 7 chocolate bars)

Now, let's solve this system of equations.

### Step 1: Simplify Equation 1
We can simplify the first equation by dividing everything by 4:
\[
x + y = 2 \quad \text{(Equation 1 simplified)}
\]

### Step 2: Solve for one variable
Solve for $ x $ in terms of $ y $ from the simplified equation:
\[
x = 2 - y
\]

### Step 3: Substitute into the second equation
Substitute $ x = 2 - y $ into the second equation $ 2x + 7y = 8 $:
\[
2(2 - y) + 7y = 8
\]

### Step 4: Solve the equation
Simplify and solve for $ y $:
\[
4 - 2y + 7y = 8
\]
\[
4 + 5y = 8
\]
\[
5y = 4
\]
\[
y = \frac{4}{5} = 0.80
\]

### Step 5: Find $ x $
Now, substitute $ y = 0.80 $ back into $ x = 2 - y $:
\[
x = 2 - 0.80 = 1.20
\]

### Final Answer:
- The cost of a can of soft drink is $ x = 1.20 $ dollars.
- The cost of a chocolate bar is $ y = 0.80 $ dollars.

Would you like further details or have any questions?

Here are 5 related questions to deepen understanding:
1. How would the solution change if Georgina had $10 to spend?
2. What if Georgina bought only 1 can of soft drink and 3 chocolate bars?
3. Can you derive a general method for solving systems of linear equations?
4. What happens to the solution if the price of the chocolate bar is doubled?
5. How would the cost change if there was a discount on the soft drinks?

**Tip**: Always try to simplify equations when solving systems—it reduces complexity and minimizes potential errors.

georgina has $8 to spend she discovers that she can buy either 4 cans of soft drink and 4 chocolate bars or 2 cans of soft drink and 7 chocolate bars how much does each item cost

Discover how to solve a system of equations to determine the cost of a can of soft drink and a chocolate bar. This algebraic problem involves setting up two equations and using the substitution method to find the solution. Suitable for Grades 8-10 students.

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