How much does a liter of milk cost, and how much does a loaf of bread cost?

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 prices, for a total of $10.

Answer 1

You start by setting up the two equations: First, 3 liters of milk and 5 loaves of bread cost $11, which can be represented as 3m + 5b = 11. The second equation would therefore be 4m + 4b = 10. There are a few ways to solve system of equations. What I usually do is solve for a variable (in terms of the second variable) and plug it into the second equation:

Solving for b from the first equation:

3m + 5b = 11

5b = 11 - 3m

b = (11 - 3m)/5

Plugging this value of b into the second equation:

4m + 4b = 10

4m + 4[(11 - 3m)/5] = 10

4m + (44/5) - (12m/5) = 10

(8m/5) = (6/5)

m = 6/8 = 3/4 = $0.75

This represents the cost of milk. Now that you have the cost of milk, you can find the cost of bread by plugging 0.75 into the equation you found for b:

b = (11 - 3m)/5

b = (11 - 3(3/4))/5

b = (11 - (9/4))/5

b = (35/4)/5

b = 7/4 = $1.75

 

You can double check that these are the correct values:

3(0.75) + 5(1.75) = 2.25 + 8.75 = 11 <---- Checks out!

4(0.75) + 4(1.75) = 3 + 7 = 10 <----- Checks out!