Question

The day before a show, a theatre had sold adult and child tickets in the ratio 8:3. On the day of the show, the theatre sold 30 more adult tickets and no more child tickets. The ratio of adult to child tickets sold became 7 : 2. Work out how many adult tickets had been sold the day before the show ?

A)86
B)90
C)94
D)96

Answer 1

The number of adult tickets sold the day before the show was D) 96.

Step-by-step explanation:

Let's assume the number of adult tickets sold the day before the show is 8x, and the number of child tickets is 3x, where x is a common multiple. On the day of the show, the theatre sold 30 more adult tickets, so the ratio of adult to child tickets became (8x + 30):(3x). According to the question, this ratio is also equal to 7:2. Setting up an equation:

(8x + 30)/(3x) = 7/2

Now, we can solve for x:

2(8x + 30) = 7(3x)

16x + 60 = 21x

60 = 21x - 16x

60 = 5x

x = 12

So, the number of adult tickets sold the day before the show is 8x = 8(12) = 96.