SOLUTION: Lisa and Beverly had just $5 to spend on a snack. They could have bought 2 hamburgers and 1 carton of milk with no change back or 1 hamburger and two cartons of milk with 40 cents

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Question 1135529: Lisa and Beverly had just $5 to spend on a snack. They could have bought 2 hamburgers and 1 carton of milk with no change back or 1 hamburger and two cartons of milk with 40 cents change back. How much does a carton of milk cost?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
system%282h%2Bm=5%2Ch%2B2m=4.6%29

E1%2BE2gives 3h%2B3m=9.6-----------ORh%2Bm=3.2.



Subtract that simpler equation from E1, and find h.

Subtract that same simpler equation from E2, and find m.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The other response you have so far shows one of many good algebraic solutions.

If an algebraic solution is not required, you can get some good brain exercise solving the problem with logical reasoning.

Suppose the problem were posed slightly differently so that the two girls originally planned to buy 2 hamburgers and 1 carton of milk, using the whole $5, but then they decided instead to get 2 cartons of milk and one hamburger, saving 40 cents.

So taking away that 2nd burger and replacing it with a 2nd carton of milk changed the total cost downwards by 40 cents. That means the hamburger cost 40 cents more than the carton of milk.

Now use that knowledge, along with either version of the order, to determine the cost of each hamburger and each carton of milk.

The second version of their order was 1 burger and 2 cartons of milk, for a total of $4.60. The burger cost 40 cents more than each carton of milk; that means 3 cartons of milk would cost $4.60-$0.40 = $4.20. And that makes the cost of each carton of milk $4.20/3 = $1.40.

Then you can find the cost of each burger using that in either of the original orders.

And here is another solution by logical reasoning that works nicely for this problem.

We know...
(1) 2 burgers and 1 milk cost $5.00
(2) 1 burger and 2 milks cost $4.60

From this we can see that exchanging a burger for a milk reduces the total cost by $0.40; or exchanging a milk for a burger increases the cost by $0.40.

But that means

(3) 3 burgers and no milk would cost $5.00+$0.40 = $5.40 -- making the cost of each burger $5.40/3 = $1.80; and
(4) 0 burgers and 3 milk would cost $4.60-$0.40 = $4.20 -- making the cost of each milk $4.20/3 = $1.40