You can start with two equations in two variables, use one to set up a substitution to get all the variables in terms of one variable as follows
Equation 1 for the Total number of tickets sold
x = child tickets
y = adult tickets
x + y = 140
So
y = 140 - x
Equation 2 for the Total Cost
5.40x = child admission cost
9.00y = adult admission cost
5.40x + 9.00y = 1036.80
We can substitute 140 - x for y in Equation 2
5.40x + 9(140 - x) = 1036.80
5.40x + 1260 - 9.00x = 1036.80
Combine like terms
1260 - 3.60x = 1036.80
Subtract 1260 from both sides of the equation
-3.60x = -223.20
Divide both sides by -3.60 to solve for x
x = -223.20/-360 = 223.20/3.60
x = 62
Substitute 62 for x in Equation 1 to solve for y
x + y = 140
62 + y = 140
Subtract 62 from both sides of the equation
y = 140 - 62
y = 78
62 Child tickets and 78 Adult tickets were sold
Checking
5.40(62) + 9.00(78) = 1036.80
334.80 + 702.00 = 1036.90
1036.80 = 1036.80
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