Question

PLZ I NEED HELP BUT PLZ EXPLAIN WHEN YOU ANSWER

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?

Answer 1

Here’s the more basic thing you need to know.

3m + 5b = 11
3(.75) + 5(1.75) = 11
2.25 + 8.75 = 11
11 = 11

4m + 4b = 10
4(.75) + 4(1.75)=10
3 + 7 = 10
10 = 10

Let m = cost of a liter of milk
Let b = cost of a loaf of bread

Bhavik bought 3 liters of milk and 5 loaves of bread
for a total of $11 so:
3m + 5b = 11

Prices didn't change and he bought 4 liters of milk
and 4 loaves of bread for $10 a month later so:
4m + 4b = 10

We have two equations:

3m + 5b = 11 equation 1
4m + 4b = 10 equation 2

To eliminate a variable we want the coefficients to add to zero.
Multiply equation 1 by 4 and equation 2 by -3. This will give us
12m in the first equation and -12m in the 2nd equation so that
we can then add the two and eliminate the m variable, thus
allowing us to solve for b.

12m + 20b = 44 4(equation 1)
-12m - 12b = -30 -3(equation 2)
--------------------
0m + 8b = 14 sum of the equations

8b = 14
b = 14/8
b = 1.75

A loaf of bread costs $1.75

Substitute that value into one of the original 2 equations
and solve for m

4m + 4b = 10
4m + 4(1.75) = 10
4m + 7 = 10
4m = 3
m = 3/4
m = .75

A liter of milk costs $.75
A loaf of bread costs $1.75

Answer 2

Explanation:

Let's convert this statement into a system of two equations

3 * (cost of a liter of milk) + 5 * (cost of a loaf of bread) = $11

4 * (cost of a liter of milk) + 5 * (cost of a loaf of bread) = $10

cost of a liter of milk = x

cost of a loaf of bread = y

3x + 5y = 11

4x + 4y = 10

You can now solve this using either substitution or elimination

I'll use elimination. Let's say I want to get rid of the x first. I need to choose numbers to multiply by the top and bottom equations to eliminat the x's. The easiest way to do this is to multiply them by each other. So we'll multiply the top by 4 and the bottom by 3. We'll need to make sure the signs are opposite as well so I'll make that a negative 3 on the bottom.

4 * (3x + 5y = 11)

-3 * (4x + 4y = 10)

12x + 20y = 44

-12x - 12y = -30

Now add straight down

0x + 8y = 14

8y = 14

y = 14/8 = $1.75

Now we can plug this back in to either equation to find the x. I'll choose the second equation

4x + 4*(1.75) = 10

4x + 7 = 10

4x = 3

x = 3/4 = $0.75

So, cost of a liter of milk = x = $0.75

and cost of a loaf of bread = y = $1.75