SOLUTION: Two groups of people order food at a restaurant. One group orders 4 hamburgers and 7 sandwiches for $34.50. The other group orders 8 hamburgers and 3 sandwiches for $30.50. Find

Algebra ->  Systems-of-equations -> SOLUTION: Two groups of people order food at a restaurant. One group orders 4 hamburgers and 7 sandwiches for $34.50. The other group orders 8 hamburgers and 3 sandwiches for $30.50. Find      Log On


   



Question 433086: Two groups of people order food at a restaurant. One group orders 4 hamburgers and 7 sandwiches for $34.50. The other group orders 8 hamburgers and 3 sandwiches for $30.50. Find the cost of each item.
Thank you :)

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = cost of sandwich
Let b = cost of hamburger
given:
(1) +7a+%2B+4b+=+34.5+
(2) +3a+%2B+8b+=+30.5+
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Multiply both sides of (1) by 2
and subtract (2) from (1)
(1) +14a+%2B+8b+=+69+
(2) +-3a+-+8b+=+-+30.5+
+11a+=+38.5+
+a+=+3.5+
Plug this back into (1) or (2)
(2) +3%2A3.5+%2B+8b+=+30.5+
+10.5+%2B+8b+=+30.5+
+8b+=+20+
+b+=+2.5+
The cost of a sandwich is $3.50
The cost of a hamburger is $2.50