Question

24 A cinema has 400 seats.

A film is shown at 5pm and at 7pm with two types of tickets available, adult and child.
At the 5pm showing of the film
The ratio of tickets sold to adults to tickets sold to children is 5:3
120 tickets are sold to children.
At the 7pm showing of the film
The number of adult tickets sold is 15% less than at 5pm
The number of child tickets sold is 10% more than at 5pm
Show that at the 7pm showing more than
of the seats are used.
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Answer 1

Answer + Step by Step explanation:

I did this question earlier in school and am happy to explain it to you, it was a hard one.

First:

3/4 of 400 = 300

because you do 400 divide the denominator (4) which is 100. Then times by the numerator (3) which is 300. So at least 300 seats must be used.

Then: Work out how many children and adult tickets were sold at 5pm.

Children tickets = 120 (given in the question)

Adult tickets = 120 ÷ 3 = 40 (to find the number that was multiplied by 3 to get 120)

So adult tickets = 40 x 5

Adult tickets = 200

next:

7pm adult tickets sold: 15% less than 200

to find 15% reduction from 200:

15 - 100 = 85

85 x 200

17,000

17,000 ÷ 100 = 170

170 - 200 =

30 adult tickets at 7pm.

children tickets sold at 7pm = 10% more than 5pm tickets

to increase by 10%

120 x 1.10 = 132 (with calculator)

120 x 11 = 1320 then ÷10 = 132 (no calculator)

132 + 170 = 302

302 ≥ 300

More than 3 quarters of the cinema seats were used.