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
Answers
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
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Answer:
I hope it's help you okkkk
