Bhavik bought
\[3\] liters of milk and
\[5\] loaves of bread for a total of
\[\$11\]. A month later, he bought
\[4\] liters of milk and
\[4\] loaves of bread at the same prices, for a total of
\[\$10\].
How much does a liter of milk cost, and how much does a loaf of bread cost?
A liter of milk costs
\[\$\]
and a loaf of bread costs
\[\$\]
.

Let's define the following variables:
- $ m $: the cost of one liter of milk (in dollars)
- $ b $: the cost of one loaf of bread (in dollars)

We are given two pieces of information that can be formulated into a system of linear equations:

1. Bhavik bought 3 liters of milk and 5 loaves of bread for a total of \$11:
   \[
   3m + 5b = 11
   \]

2. A month later, Bhavik bought 4 liters of milk and 4 loaves of bread for a total of \$10:
   \[
   4m + 4b = 10
   \]

We can solve these equations simultaneously to find the values of $ m $ and $ b $.

First, let's simplify the second equation by dividing every term by 4:
\[
m + b = 2.5
\]

Now we have:
\[
3m + 5b = 11 \quad \text{(1)}
\]
\[
m + b = 2.5 \quad \text{(2)}
\]

We can solve equation (2) for $ m $:
\[
m = 2.5 - b
\]

Next, substitute $ m $ from equation (2) into equation (1):
\[
3(2.5 - b) + 5b = 11
\]

Expand and simplify:
\[
7.5 - 3b + 5b = 11
\]
\[
7.5 + 2b = 11
\]

Subtract 7.5 from both sides:
\[
2b = 3.5
\]

Divide both sides by 2:
\[
b = 1.75
\]

Now substitute $ b = 1.75 $ back into equation (2) to find $ m $:
\[
m + 1.75 = 2.5
\]
\[
m = 2.5 - 1.75
\]
\[
m = 0.75
\]

Thus, the cost of one liter of milk is $ \$0.75 $ and the cost of one loaf of bread is $ \$1.75 $.

So,
- A liter of milk costs $ \$0.75 $.
- A loaf of bread costs $ \$1.75 $.

Would you like more details or have any questions?

Here are 8 related questions to expand your understanding:

1. How do you solve a system of linear equations using substitution?
2. Can you solve the same problem using the elimination method?
3. What are some real-world applications of solving systems of linear equations?
4. How can you verify the solution to a system of equations?
5. What is the graphical interpretation of solving a system of linear equations?
6. How do you set up a system of equations from a word problem?
7. What are the differences between dependent, independent, and inconsistent systems of equations?
8. How do changes in prices affect the solutions of the system of equations in this context?

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

Learn how to solve a system of linear equations to find the cost of milk and bread based on quantities purchased and total expenditures. This problem involves using the substitution method to solve equations. Suitable for students in Grades 7-9.

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