SOLUTION: The grocery store we use does not mark prices on its goods.My wife went to this​ store, bought two packages of bacon and five cartons of eggs, and paid a total of $14.03. No

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Question 1131279: The grocery store we use does not mark prices on its goods.My wife went to this​ store, bought two packages of bacon and five cartons of eggs, and paid a total of $14.03. Not knowing that she went to the store, I also went to the same store, purchased five packages of bacon and two cartons of eggs, and paid a total of $19.43. Now we want to return two packages of bacon and two cartons of eggs. How much will be refunded?
Found 2 solutions by josmiceli, ikleyn:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = cost in dollars/pkg of bacon
Let +b+ = cost in dollars/carton of eggs
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(1) +2a+%2B+5b+=+14.03+
(2) +5a+%2B+2b+=+19.43+
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Multiply both sides of (1) by +2+
Multiply both sides of (2) by +5+
Subtract (1) from (2)
(2) +25a+%2B+10b+=+97.15+
(1) +-4a+-+10b+=+-28.06+
----------------------------------
+21a+=+69.09+
+a+=+3.29+
and
(1) +2%2A3.29+%2B+5b+=+14.03+
(1) +6.58+%2B+5b+=+14.03+
(1) +5b+=+7.45+
(1) +b+=+1.49+
-------------------------------------
Return 2 pkgs of bacon for: +2a+=+6.58+
Return 2 cartons of eggs for: +2b+=+2.98+
----------------------------------------------------
check:
(1) +2a+%2B+5b+=+14.03+
(1) +2%2A3.29+%2B+5%2A1.49+=+14.03+
(1) +6.58+%2B+7.45+=+14.03+
(1) +14.03+=+14.03+
---------------------------------------
(2) +5a+%2B+2b+=+19.43+
(2) +5%2A3.29+%2B+2%2A1.49+=+19.43+
(2) +16.45+%2B+2.98+=+19.43+
(2) +19.43+=+19.43+
OK

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
2B + 5C = 14.03      (1)
5B + 2C = 19.43      (2)


Add the equation (both sides). You will get


7B + 7C = 14.03 + 19.43


7*(B+C) = 33.46


Now divide both sides by 7:


B + C = 4.78.


Now multiply both sides by 2. You will get


2B + 2C = 9.56.    It is your ANSWER.


Answer.  $9.56.

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This problem was specially designed to teach you do not make unnecessary calculations when solving it.

Calculating the prices of EACH item is NOT required in this problem.
Making these calculations is UNNECESSARY work.

The problem should be solved exactly in a way as presented in my post.

It is IMPORTANT you understand it.


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