SOLUTION: A group of 18 people ordered soup and sandwiches for lunch. Each person in the group had either one soup or one sandwich. The sandwiches cost $7.75 each and the soups cost $4.50 ea

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A group of 18 people ordered soup and sandwiches for lunch. Each person in the group had either one soup or one sandwich. The sandwiches cost $7.75 each and the soups cost $4.50 ea      Log On


   

Question 997435: A group of 18 people ordered soup and sandwiches for lunch. Each person in the group had either one soup or one sandwich. The sandwiches cost $7.75 each and the soups cost $4.50 each. If the total cost of all 18 lunches was 113.50, bow many sandwiches were ordered?
Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
Let's call soup x and sandwich y:
x+y= 18 Subtract y from both sides and we get:
x= 18-y
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4.50x= 7.75y= 113.50 Let's in this formula substitute the value of x per above:
4.50(18-y)+7.75y= 113.50
81-4.50y+7.75y= 113.50 Subtract 81 on both sides and add y on left
3.25y= 32.5 Divide both sides by 3.25
y= 10 They ordered 10 sandwiches
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Proof:
10*7.75= 77.5
18-10=8soups*4.50= 36
77.5+36=113.50 We have the correct answer