The manager at a concert venue keeps track of the number of adult tickets and student tickets sold each day and the total money received. On Tuesday, a total of 89 tickets were sold, and the money collected was $1,119. If adult tickets are sold for $15 and student tickets are sold for $11, how many adult tickets and student tickets were sold?

A=number of adult tickets

s=number of student tickets

so

total of 89 tickets sold

a+s=89

total collected was 1119

15a+11s=1119

so we have

a+s=89

15a+11s=1119

subsitution

a+s=89

minus s from both sides

a=89-s

subsitte 89-s for a in the other equation

15a-11s=1119

15 (89-s) + 11s=1119

1335-15s+11s=1119

1335-4s=1119

minus 1335 from both sides

-4s=-216

divide both sides by - 4

s=54

subsitute back

a=89-s

a=89-54

a=35

35 adult tickets

54 student tickets