Amovie theater sells student tickets for $6 and adults for $8. the theater sold 140 tickets, generating $990. how many student tickets were sold

65 student tickets were sold

Solution:

Given that movie theater sells student tickets for $ 6 and adults for $ 8

Let "s" be the number of student tickets sold

Let "a" be the number of adult tickets sold

Cost of 1 student ticket = $ 6

Cost of 1 adult ticket = $ 8

Given that theater sold 140 tickets

Number of student tickets sold + number of adult tickets sold = 140

s + a = 140 ------ eqn 1

The theater generated $ 990

number of student tickets sold x Cost of 1 student ticket + number of adult tickets sold x Cost of 1 adult ticket = 990

6s + 8a = 990 ------ eqn 2

Let us solve eqn 1 and eqn 2 to find values of "s" and "a"

From eqn 1,

s = 140 - a ----- eqn 3

Substitute eqn 3 in eqn 2

6(140 - a) + 8a = 990

840 - 6a + 8a = 990

2a = 150

a = 75

Substitute a = 75 in eqn 3

s = 140 - 75

s = 65

Therefore 65 student tickets were sold

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