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

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) (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) (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
RELATED QUESTIONS
A large family went to a restaurant for a buffet dinner the price of the dinner was $12... (answered by ikleyn)
An amusement park charges one admission price for adults and another admission price for... (answered by josgarithmetic)
2 families had buffet lunch at Universe Restaurant. One of the families with 3 adults and (answered by josgarithmetic)
In this activity, you will create quadratic inequalities in one variable and use them to... (answered by josmiceli)
the johnson family and the gonzalez family went to the movies together. the johnson... (answered by addingup)
The cost for 2 adults and 5 children to eat at the local buffet restaurant is $46.50.... (answered by Boreal)
At a restaurant one family ordered 6 burgers and 5 fries, paying $68. Another family... (answered by jorel1380,josgarithmetic)
A family of 4 (2 children and 2 adults) went to the aquarium. If each adult ticket costs... (answered by checkley79)
A restaurant charges $7 for a regular meal and $5 for a child's meal. Both include tax. A (answered by josmiceli)