Question 1139294: A large family went to a restaurant for a buffet dinner the price of the dinner was $12 for adults and $8 for children it's a total bill for a group of 13 people came to $136 how many children were in the group
Answer by ikleyn(52803)   (Show Source):
You can put this solution on YOUR website! .
Let "a" be the number of adults and "c" be the number of children in the group.
Then from the condition, you have this system of two equations in two unknowns
a + c = 13 (1) (counting persons)
12a + 8c = 136 (2) (counting dollars)
To solve the system, multiply eq(1) by 8 (both sides). Keep equation (2) as is. You will get
8a + 8c = 13*8 (3)
12a + 8c = 136 (4) (the same as (2) )
Subtract eq(3) from eq(2). You will get
12a - 8a = 136 - 13*8
4a = 32
a = 32/4 = 8.
ANSWER. There were 8 adults in the group and the rest, 13 - 8 = 5, were children.
CHECK. 8*12 + 5*8 = 136 dollars. ! Correct !
Solved.
There are other ways / methods to solve this problem.
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To see many other similar problems and the methods of its solution, look into the lessons
- Using systems of equations to solve problems on tickets
- Three methods for solving standard (typical) problems on tickets
in this site.
From these lessons, learn on how to solve such problems once for all.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic "Systems of two linear equations in two unknowns".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.
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