Answer: 65 adult ticket and 24 children's ticket
Step-by-step explanation:
Let the total number of adults be x
And the total number of children be y
The cost of ticket for 1 adult = $4.10 , this means that the cost of ticket for x adults will be 4.10x
The cost of ticket for a child = $2.70 , this means that the cost of ticket for y children will be 2.70y.
The total sale was $331.30 , that is
4.10x + 2.70y = 331.30
Total number of movie watchers were 89 , that is
x + y = 89
Combining the two equations , we have :
x + y = 89 ......................... equation 1
4.10x + 2.70y = 331.30 .................. equation 2
solving the system of linear equation by substitution method.
From equation 1 , make x the subject of the formula
x = 89 - y ........................... equation 3
substitute x = 89 - y into equation 2 , equation 2 then becomes
4.10(89 - y ) + 2.70y = 331.30
expanding the bracket , we have
364.9 - 4.10y + 2.70y = 331.30
364.9 - 1.4y = 331.30
collecting the like terms , we have
364.9 - 331.30 = 1.4y
33.6 = 1.4y
divide through by 1.4
33.6/1.4 = y
Therefore : y = 24
substitute y = 24 into equation 3
x = 89 - y
x = 89 - 24
x = 65
Therefore , there were 65 adults and 24 children ticket sold
