SOLUTION: 30 people went in a group to the zoo. Adults' tickets were $6 and children paid $2. Altogether $84 was paid for entrance fees. How many children and how many adults were in the par

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Question 765303: 30 people went in a group to the zoo. Adults' tickets were $6 and children paid $2. Altogether $84 was paid for entrance fees. How many children and how many adults were in the party. How do I solve this problem using algebra?
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Identify all the numbers. What kinds of units are used? What are counted?

People, ticket prices, cost in entrance fees...

A = $6 per adult
C = $2 per child
a = how many adults___UNKNOWN
c = how many children____UNKNOWN
p = 30 people, the total of a+c
R = the entrance fee total for these p people, $84

Study the problem description and the variables assignments before you continue.

ACCOUNT FOR ENTRANCE COST:
A%2Aa%2BC%2Ac=R

ACCOUNT FOR QUANTITY OF PEOPLE:
a%2Bc=p

You have two equations and two unknown variables, both equations linear, so just solve the system for a and c:
---------------
SYSTEM
--------------
highlight%28A%2Aa%2BC%2Ac=R%29
highlight%28a%2Bc=p%29
--------------

How you go about solving for a and c depends on what methods you know currently. Some students may prefer to substitute the known values early and perform the solving in that way. Either way, you could solve the people equation for either a or c and substitute this into the cost equation and solve through for the other variable to get its value; and then use this value to solve for the other still unknown variable.