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. how much does a liter of milk cost, and how much does a loaf of bread cost? a liter of milk costs $\square$ and a loaf of bread costs $\square$. show calculator

Explanation:

Step1: Define variables for costs

Let $m$ = cost of 1L milk, $b$ = cost of 1 loaf bread.

Step2: Set up system of equations

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

Step3: Simplify second equation

Divide by 4: $m + b = \frac{10}{4} = 2.5$, so $m = 2.5 - b$.

Step4: Substitute $m$ into first equation

$$3(2.5 - b) + 5b = 11$$
$$7.5 - 3b + 5b = 11$$
$$7.5 + 2b = 11$$

Step5: Solve for $b$

$$2b = 11 - 7.5 = 3.5$$
$$b = \frac{3.5}{2} = 1.75$$

Step6: Solve for $m$

$$m = 2.5 - 1.75 = 0.75$$

Answer:

A liter of milk costs $\$0.75$ and a loaf of bread costs $\$1.75$.