Question

A movie theater has a seating capacity of 257. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 1860, How many children, students, and adults attended? children attended. students attended. adults attended.

Answer 1

Children = 122

Students = 74

Adults = 61

Explanation:

Given

Seating capacity = 257

Charges: Children = $5.00; Students = $7.00; Adults = $12.00

Total sales of ticket = $1860

Required:

Number of children, students and adults present in the theatre.

Let A, C and S represent adult, children and student respectively.

There are half as many adults as there are children; this means that

A = ½C

If the total seat capacity is 257, then

A + C + S = 257

Also, if the total sales of tickets is $1860, then

12A + 7S + 5C = 1860

So, we have two equations to be solved simultaneously.

A + C + S = 257 --- (1)

12A + 7S + 5C = 1860 --- (2)

Substitute ½C for A in (1) and (2)

½C + C + S = 257

Multiply both sides by 2

2(½C + C + S) = 2 * 257

C + 2C + 2S = 514

3C + 2S = 514 ----- (3)

12(½C) + 7S + 5C = 1860

6C + 7S + 5C ,= 1860

6C + 5C + 7S = 1860

11C + 7S = 1860 --- (4)

Make S the subject of formula in (3)

2S = 514 - 3C

S = ½(514 - 3C)

S = 257 - 1.5C

Substituton 257 - 1.5C for S in (4)

11C + 7(257- 1.5C) = 1860

11C + 1799 - 10.5C = 1860

Collect like terms

11C - 10.5C = 1860 - 1799

0.5C = 61

Multiply both sides by 2

2 * 0.5C = 2 * 61

C = 122

Recall that

S = 257 - 1.5C

S = 257 - 1.5(122)

S = 257 - 183

S = 74

Also recall that

A = ½C

A = ½ * 122

A = 61

Hence the attendance at the mobie theatre are;

Children = 122

Students = 74

Adults = 61