Question

Tickets prices for a science museum are $18 for adults and $12 for students. If $162 is collected from a group of 12 people, how many adults and students are in a group?

Answer 1

X=number of adults, y= number of students

x+y=12
18x+12y=162

You can simplify the second equation by dividing by six: 3x+2y=27
Rearrange the first equation: y= 12-x. Plug y into the simplified second equation:

3x+2(12-x)=27
3x-2x+24=27
x=3.

Plug the now known x value into y=12-x. So y= 9.
Therefore, there are 3 adults and 9 students.