Algebra equations

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 bread at the same prices, for a total of $10

Answer 1

What we can use to solve this is a system of equation:

let 1liter of milk be x and 1 loaf of bread be y.

3x+5y=11

4x+4y=10

I used different variables because the loaves of bread and the milk have different costs. To solve this. we basically need to cancel one variable out. Let's cancel x. to do that, we need a least common multiple, which is 12. A system of equations is usually added, so we need a two numbers that when added will cancel out the x's. That would be -12 and 12. To get -12 on the first equation, we multiply the whole thing by -4, and to get 12 on the bottom equation, we multiply that whole equation by 3. The x's cancel out and we're left with this:

-20y=-44

12y=30

Then we add the two equations and get:

-8y=-14. To solve for y, we simply divide by -8 on both sides, and the y is 1.75, or in currency, $1.75. Because we said that the y would represent the loaf of bread, this is the cost of each loaf of bread. To find the cost of each liter of milk, we simply plug the y back into either one of the equations to solve for x. Note that you can't solve for y and x at the same time, which is why we first cancelled out the x to solve for y. Now we're looking for x, and we already have the y, which is $1.75. I'll pick the bottom equation to plug it into. Here's what we get:

4x+4(1.75)=10 Notice that i plugged in the $1.75 for y to find x.

Then we get: 4x+7=10. We subtract 7 for both sides and we're left with 4x=3. We now divide each side by 4, and we get 0.75. Therefore, each liter of milk costs 75 cents. To verify your answer you can plug in the x(0.75) and the y(1.75) in either equation, and you should get the total value on the right side of the equation. Hope this was helpful!