Question

Bhavik bought 333 liters of milk and 555 loaves of bread for a total of \$11$11dollar sign, 11. A month later, he bought 444 liters of milk and 444 loaves of bread at the same prices, for a total of \$10$10dollar sign, 10.
How much does a liter of milk cost, and how much does a loaf of bread cost?
A liter of milk costs \$$dollar sign
and a loaf of bread costs \$$dollar sign
.

Answer 1

Answer:

Milk costs 75 cents per litre.

Bread costs $1.75 per loaf.

Step-by-step explanation:

I think there has been an issue with repetition here.  I suspect the problem is:

• 3 litres of milk and 5 loaves of bread cost $11
• 4 litres of milk and 4 loaves of bread cost $10
• Find the cost of a litre of milk and the cost of a loaf of bread.

Let m be the cost of a litre of milk.

Let b be the cost of a loaf of bread.

The first condition says:  3m + 5b = 11          ... (1)

The second condition says:  4m + 4b = 10     ... (2)

Right away, we can make equation (2) tidier by dividing through by 2 to get:

2m + 2b = 5   ... (3)

We want to use (1) and (3) to get m and b.

Working towards cancelling m, multiply (1) by 2 and multiply (3) by 3 to get:

6m + 10b = 22     ... (4)

6m + 6b = 15      ... (5)

Now subtracting (5) from (4) gives

4b = 22 - 15 = 7  =>  b = 7/4 = 1.75    ... (*)

Use any equation above to then get m.  For instance, from (3):

2m = 5 - 2b = 5 - 2 × 1.75 = 5 - 3.5 = 1.5  =>  m = 0.75   ... (**)

Equations (*) and (**) together give us our solution:

b = 1.75  and  m = 0.75