Question

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 price for a total of $10. How much does a liter of milk cost and how much does a loaf of bread cost?

Answer 1

Let the price of 1 liter of milk be m, and let the price of 1 loaf of bread be b.

3 liters of milk cost 3m.
5 loaves of bread cost 5b.
The total is $11.
That gives us the first equation:

3m + 5b = 11

4 liters of milk cost 4m.
4 loaves of bread cost 4b.
The total is $10.
That gives us the second equation:

4m + 4b = 10

We have a system of two equations.

3m + 5b = 11
4m + 4b = 10

Multiply the first equation by -4.
Multiply the second equation by 3.
Then, add the equations.

      -12m - 20b = -44
  +   12m + 12b = 30
---------------------------
                   -8b = -14

b = 14/8 = 7/4 = 1.75

Now substitute b with 1.75 in the first original equation.

3m + 5b = 11

3m + 5(1.75) = 11

3m + 8.75 = 11

3m = 2.25

m = 0.75

Answer: A liter of milk costs $0.75, and a loaf of brad costs $1.75.