Sixty-three tickets were sold for an upcoming school play. Adult tickets are $3.75 and student tickets are $1.75. A total of $194.25 was made in ticket sales. How many adult tickets were sold?

Answer 1

A+S = 63

S=63-A

3.75A + 1.75S = 194.25

3 3/4 A + 1 3/4 S = 194 1/4

(15/4)A + (7/4)S = 777/4

15A + 7S = 777

15A + 7(63-A) = 777

8A = 777- 441 = 336

A = 336/8 = 42

A = 42 adult tickets

S = 63-42 = 21 student tickets

Answer 2

Answer : 42 Adults tickets were sold

Process:

Adults Tickets = x

Student tickets = y

x+y = 63

3.75x + 1.75y = 194.25

multiply (x+y=63) by 1.75 to get (1.75x+1.75y=110.25)

subtract (3.75x+1.75y=194.25) and (1.75x+1.75y=110.25) to get (2x=84)

This gives us x=42, and since x is the amount of adult tickets sold that we originally specified, we know that 42 adult tickets were sold for the upcoming school play.

Answer 3

x = number of adult tickets sold

y = number of student tickets sold

Set up the system of linear equations.

3.75x + 1.75y = 194.25

x + y = 63

Find the number of adult tickets sold. Use substitution method by subtracting y on both sides in Equation #2 to get x = 63 - y. Plug the equation into Equation #1 as follows:

3.75(63 - y) + 1.75y = 194.25

236.25 - 3.75y + 1.75y = 194.25

236.25 - 2y = 194.25

-2y = -42

y = 21

21 adult tickets were sold for the upcoming school play.