Question

Afternoon Show Evening Show
Adult $32 $36
Child $18 $22
andrew spends $196 on tickets for an evening show. How many adult and child tickets does he buy

Answer 1

Given :

          Afternoon Show  Evening Show

Adult            $32                $36

Child             $18                 $22

andrew spends $196 on tickets for an evening show.

To Find : How many adult and child tickets does he buy

Solution:

Let say Adult tickets  = A

and Child ticket = C

Adult ticket cost in evening show = 36

Hence  cost = 36A

Child ticket cost in evening show = 22

Hence  cost = 22C

36A + 22C  = 196

=> 18A  + 11C  = 98

=> 11A  + 11C   = 98 - 7A

=> 11 (A + C)  = 99  - (1 + 7A)

=> 11 (A + C) = 11 * 9  -  (1 + 7 A)

(1 + 7 A)  must be multiple of 11

Hence  1  + 7A  = 11k

=> 7A  = 11k  - 1

=> 7A  = 7k  + (4k - 1)

Hence 4k - 1 must be multiple of 7

4k - 1 = 7m

4k = 7m + 1  = 8m - m + 1 = 4 (2m) + ( 1 - m)

=>  m = 1 hence  k = 2  

7A  = 11k  - 1

=> 7A = 21

=> A = 3

18A  + 11C  = 98

=> 54 + 11C =  98

=> 11C = 44

=> C = 4

Hence 3 Adult tickets and 4 child ticket bought

Verification :

36 x  3 + 22 x 4 = 108 + 88 = 196

Learn More:

कितने लड्डू

https://brainly.in/question/16616318

A farmer has 5 cows numbered 1 to 5 no 1 cow gives 1kg milk ... no

brainly.in/question/16418161

Answer 2

Answer:

I hope it's help you okkkk