SOLUTION: Hi! I really need help with this problem. At Lisa's sandwich Shop, two chicken sandwiches and four cheese sandwiches cost $18. Five chicken sandwiches and six cheese sandwiches c

Algebra ->  Linear-equations -> SOLUTION: Hi! I really need help with this problem. At Lisa's sandwich Shop, two chicken sandwiches and four cheese sandwiches cost $18. Five chicken sandwiches and six cheese sandwiches c      Log On


   



Question 1037104: Hi! I really need help with this problem.
At Lisa's sandwich Shop, two chicken sandwiches and four cheese sandwiches cost $18. Five chicken sandwiches and six cheese sandwiches cost $34. Which type of sandwich is more expensive, and by how much?
Thanks!

Found 2 solutions by ikleyn, josmiceli:
Answer by ikleyn(52813) About Me  (Show Source):
You can put this solution on YOUR website!
.
Hi! I really need help with this problem.
At Lisa's sandwich Shop, two chicken sandwiches and four cheese sandwiches cost $18.
Five chicken sandwiches and six cheese sandwiches cost $34. Which type of sandwich is more expensive, and by how much?
Thanks!
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

2x + 4y = 18,    (1)
5x + 6y = 34.    (2)

Multiply the first eqn by 3%2F2 (both sides). You will get

3x + 6y = 27,    (1')
5x + 6y = 34.    (2').

Now, distract eqn (1') from (2'). You will get

2x = 34 - 27 = 7.

From this point, please complete the solution on your own.


Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = price of a chicken sandwich
Let +b+ = price of a cheese sandwich
-------------------------
(1) +2a+%2B+4b+=+18+
(2) +5a+%2B+6b+=+34+
-----------------------
Multiply both sides of (1) by +3+
Multiply both sides of (2) by +2+
Then subtract (1) from (2)
-----------------------------
(2) +10a+%2B+12b+=+68+
(1) +-6a+-+12b+=+-54+
-----------------------
+4a+=+14+
+a+=+3.5+
------------------
Substitute this result into (1)
(1) +2a+%2B+4b+=+18+
(1) +2%2A3.5+%2B+4b+=+18+
(1) +7+%2B+4b+=+18+
(1) +4b+=+11+
(1) +b+=+2.75+
------------------
The chicken sandwich is more expensive by 75 cents
+3.5+-+2.75+=+.75+
-------------------------
check:
(1) +2a+%2B+4b+=+18+
(1) +a+%2B+2b+=+9+
(1) +3.5+%2B+2%2A2.75+=+9+
(1) +3.5+%2B+5.5+=+9+
(1) +9+=+9+
OK
You can check (2)