Question

Last Tuesday,regal cinemas sold a total of 90 movie tickets proceeds totaled $560.Tickets can be bought in one of 3 ways:a matinee admission costs$5,students admission is $6 all day,and regular admissions are $7.How many regular tickets were sold if twice as many regular tickets were sold as matinee tickets

Answer 1

number of regular tickets sold is 40

Step-by-step explanation:

Total movie tickets = 90

Earnings from the 90 tickets = $560

cost for matinee admission = $5

let the number of matinee admission tickets = m

cost for students admission = $6

let the number of students admission = s

cost for regular admission = $7

let the number of regular admission = r

$5(m) + $6(s) + $7(r) = Total earnings from the sales of all tickets

5m + 6s + 7r = 560 ...(1)

m + s + r = total tickets

m + s + r = 90 ...(2)

Twice as many regular tickets were sold as matinee tickets:

r = 2(m)

r = 2m ...(3)

substitute for r in equation (1) and (2):

5m + 6s + 7(2m) = 560

5m + 6s + 14m = 560

19m + 6s = 560 ...(*1)

m + s + 2m = 90

3m + s = 90 ...(*2)

From (*2), we will make s the subject of formula:

s = 90 - 3m

substitute for s in (*1):

19m + 6(90 - 3m) = 560

19m + 540 - 18m = 560

m + 540 = 560

m = 560 - 540

m = 20

substitute for m in (3):

r = 2(20)

r = 40

s = 90 - 3m

s = 90 - 3(20)

s = 90 - 60

s = 30

Hence, number of regular tickets sold is 40