Question

The museum charges $12.50 for youth admission and $17.50 for adults.  One day the museum collected $1535 from a total of 110 youths  and adults.  How many admissions of each type were sold?

Answer 1

x - young
y - adult


`12.50x+17.50y=1535\\ x+y=110\\\\ 12.50x+17.50y=1535\\ x=110-y\\\\ 12.50(110-y)+17.50y=1535\\ 1375-12.50y+17.50y=1535\\ 5y=160\\ y=32\\\\ x=110-32\\ x=78`