Answer:
61 adults, 122 children, and 52 students
Step-by-step explanation:
Let a = amount of adults, c = amount of children, and s = amount of students.
Let's go over what we know:
total amount: 235
twice as many children as adults
children: $5
student: $7
adult: $12
Using this information, we can determine the following:
a = 1/2c
235 = c + s + a
1706 = 5c + 7s + 12a
Since we know a = 1/2c, plug 1/2c in for a. The equations become:
235 = c + s + 1/2c
1706 = 5c + 7s + 6c
Now, solve the inequalities by substitution.
235 = c + s + 1/2c
235 = 1 1/2c + s
-s + 235 = 1 1/2c
-s = -235 + 1 1/2c
s = 235 - 1 1/2c
Now, plug in the value for s into the other equation.
1706 = 5c + 7(235 - 1 1/2c) + 6c
-5c + 1706 = 7(235 - 1 1/2c) + 6c
-5c = -1706 + 7(235 - 1 1/2c) + 6c
-5c = -1706 + 1645 - 21c/2 + 6c
-5c = -61 - 21c/2 + 6c
-5c = -61 - 9c/2
c = 122
Now, plug in the value for c into the value of s.
s = 235 - 1 1/2(122)
s = 235 - 183
s = 52
Finally, plug in the value for c into the value of a.
a = 1/2(122)
a = 61
To check, add up all values to make sure they equal 235.
61 + 52 + 122 = 235.
Therefore, the final answers are 61 adults, 122 children, and 52 students.
