SOLUTION: 5 drinks and 3 sandwiches cost $25. 6 drinks and 6 sandwiches cost $42. what is individual cost of drink and sandwich?

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Question 932826: 5 drinks and 3 sandwiches cost $25. 6 drinks and 6 sandwiches cost $42. what is individual cost of drink and sandwich?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
let drinks and sandwiches be x and y:
if 5 drinks and 3 sandwiches cost $25, then we have
5x%2B3y=25....eq.1
if 6 drinks and 6 sandwiches cost $42, then we have

6x%2B6y=42....eq.2
to find out what is individual cost of drink and sandwich, solve the system:

5x%2B3y=25....eq.1....both sides multiply by -2 then add eq.1 and eq.2
6x%2B6y=42....eq.2
______________________
-10x-6y=-50....eq.1
6x%2B6y=42....eq.2
________________________add
-10x-6y%2B6x%2B6y=-50%2B42........cancel out y
-10x%2B6x=-50%2B42
-4x=-8
x=-8%2F-4
highlight%28x=2%29...the cost of drink is $highlight%282%29
go to eq.1 or eq.2, substitute 2 for x and solve for y
6%2A2%2B6y=42....eq.2
12%2B6y=42
6y=42-12
6y=30
y=30%2F6
highlight%28y=5%29...the cost of sandwich is $highlight%285%29