SOLUTION: The Lang family and the Rogers family went to a brunch buffet. The restaurant charges one price for adults and another price for children. The Lang family has two adults and thre

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Question 191854: The Lang family and the Rogers family went to a brunch buffet. The restaurant charges one price for adults and another price for children. The Lang family has two adults and three children, and their bill was $40.50. The Rogers family has three adults and one child, and their bill was $38.00. What is the price of the buffet for an adult and the price of a child?
Found 2 solutions by checkley75, RAY100:
Answer by checkley75(3666) About Me  (Show Source):
You can put this solution on YOUR website!
2A+3C=40.50
3A+C=38.00 OR C=38.00-3A
NOW REPLACE C WITH (38.00-3A) IN THE FIRST EQUATION & SOLVE FOR A.
2A+3(38.00-3A)=40.50
2A+114.00-9A=40.50
-7A=40.50-114.00
-7A=-73.50
A=-73.50/-7
A=10.50 IS THE PRICE FOR EAXH ADULT.
2*10.50+3C=40.50
21.00+3C=40.50
3C=40.50-21.00
3C=19.50
C=19.50/3
C=6.50 IS THE PRICE FOR EACH CHILD.
PROOF:
3*10.50+6.50=38.00
31.50+6.50=38.00
38.00=38.00

Answer by RAY100(1637) About Me  (Show Source):
You can put this solution on YOUR website!
Let A = adult price
let C = Child price
1) 2A+3C=40,5
2) 3A+1C=38.00
mult (2) by 3
9A+3C=114.00
subtract (1)
7A +0C= 73.50
divide by 7, both sides of eqn
A=10.50
subst in (1)
2(10.5) + 3C = 40,50
21.00 +3C= 40.50
subtract 21.00 both sides
3C= 19.50
divide both sides by 3
C=6.50
check
2(10,50) + 3(6.50)= 21 + 19.50 = 40.50 ok
3(10.50) + 6.50 = 31.50 + 6.50 = 38.00 ok