Hey there! :)
Answer:
118 children
58 students
59 adults
Step-by-step explanation:
We can solve this problem by setting up a system of equations:
Let a = adults
2a = children (since double the # of adults were children), and
s = students
Set up the equations:
1704 = 5(2a) + 7s + 12(a)
1704 = 10a + 7s + 12a
235 = 2a + a + s
Simplify the equations:
1704 = 22a + 7s
235 = 3a + s
Subtract the bottom equation from the top by multiplying the bottom equation by 7 to eliminate the 's' variable:
1704 = 22a + 7s
7(235 = 3a + s)
1704 = 22a + 7s
1645 = 21a + 7s
---------------------- (Subtract)
59 = a
This is the number of adults. Substitute this number into an equation to solve for the number of students:
235 = 3(59) + s
235 = 177 + s
s = 58.
Since the number of children is equivalent to 2a, solve:
2(59) = 118 children.
Therefore, the values for each group are:
118 children
59 adults
58 students.
