## 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 h

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.

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2 months 2021-09-26T00:21:48+00:00 1 Answer 0 views 0

Children = 122

Students = 74

Step-by-step 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