Question

So far a total of 48 tickets have been sold for the school play for a total revenue of $220. How many student tickets have been sold? Set up and solve a system of equations to solve the problem

Answer 1

You forgot to tell us how much the tickets cost each. So I just arbitrarily chose that the price of a student ticket is $4 and the price of a non-student ticket is $6. Let the number of student tickets be x Let the number of non-student tickets be y Price Money Type Number of from of of EACH ALL ticket tickets ticket tickets ------------------------------------------- student x $4 $4x non-student y $6 $6y ------------------------------------------- TOTALS 48 ----- $220 The first equation comes from the second column. x + y = 48 The second equation comes from the last column: 4x + 6y = 220 So we have this system of equations: . We solve by substitution. Solve the first equation for y: x + y = 48 y = 48 - x Substitute (48 - x) for y in 4x + 6y = 220 4x + 6(48 - x) = 220 4x + 288 - 6x = 220 -2x + 288 = 220 -2x = -68 x = 34 = the number of student tickets. Substitute in y = 48 - x y = 48 - (34) y = 14 non-student tickets. Checking: 34 student tickets brings in $136 and 14 non-students is $84 That's 48 tickets. And indeed $136 + $84 = $220