algebra word problem.

Question

Lisa and Beverly had just $5 to spend for an after-school snack. They could have bought 2 hamburgers and 1 carton of milk with no change back or 1 hamburger and 2 cartons of milk with 40 cents change back. How much does a carton of milk cost?

Answer 1

Hi Gin,

Let's turn this word problem into some numbers to make it easier to do the math. First, we know that 2 hamburgers (let's call these h) and 1 milk (let's call this m) will cost $5 exactly. This means:

5 = 2h + m

We also know that 1 hamburger and 2 milks will give you 40 cents in change. This means the girls spent $4.60 because $5 - $.40 = $4.60. The equation would be

4.60 = h + 2m

We want to know how much a carton of milk costs, so let's rearrange the first equation to isolate m.

m = 5 - 2h

Now, we need to know how much h is. If we rearrange the second equation, we can put h in terms of m and then plug that equation into our equation for m.

h = 4.6 - 2m

Now, let's plug the equation for h into the h in our isolated m equation.

m = 5 - 2(4.6 - 2m)

Simplify the equation and you should be able to find the cost of 1 milk.

m = 5 - 9.2 + 4m

m = -4.2 + 4m

3m = 4.2

m = 0.71

One carton of milk costs 71 cents.