If tickets cost 12 dollars for students and 18 for adults and 162 dollars is collected from 12 people how many adults and students are in the group
S = Number of students
A = Number of adults
12 $ * S + 18 $ * A = 162 $
OR
12 S + 18 A = 162
S + A = 12
A = 12 - S
12 S + 18 A = 162
12 S + 18 ( 12 - S ) = 162
12 S + 18 * 12 - 18 * S = 162
12 S + 216 - 18 S = 162
12 S - 18 S = 162 - 216
- 6 S = - 54 Divide both sides by - 6
S = - 54 / - 6 = 9
A = 12 - S = 12 - 9 = 3
9 students an 3 adults
Proof :
9 * 12 $ + 3 * 18 $ = 108 $ + 54 $ = 162 $
3 adults and 9 students
To solve this problem, we can use a system of equations. Let's represent the number of students as 's' and the number of adults as 'a'.
Given that tickets cost $12 for students and $18 for adults, and a total of $162 is collected from 12 people, we can set up the following equations:
Equation 1: 12s + 18a = 162 (representing the total amount collected)
Equation 2: s + a = 12 (representing the total number of people)
Now we can solve this system of equations to find the values of 's' and 'a'.
To solve for 's', we can multiply Equation 2 by -12 and then add it to Equation 1:
-12(s + a) + 12s + 18a = -12(12) + 162
-12s - 12a + 12s + 18a = -144 + 162
6a = 18
a = 18 / 6
a = 3
Now that we have the value of 'a' (the number of adults), we can substitute it back into Equation 2 to solve for 's' (the number of students):
s + 3 = 12
s = 12 - 3
s = 9
Therefore, there are 9 students and 3 adults in the group.