Step: 1
Let x be the number of adults.
Step: 2
Let y be the number of children.
Step: 3
Total number of tickets = 209
Step: 4
So, Number of adults + Number of children = 209
Step: 5
x + y = 209
[Equation 1.]
Step: 6
Total amount collected =$1477
Step: 7
So, (Cost of an adult ticket) x (Number of adults) + (Cost of a child ticket) x (Number of children) = $1477
Step: 8
13x + 3y = 1477
[Substitute.]
Step: 9
13(-y + 209) + 3y = 1477
[Substitute -y + 209 for x in Equation 2.]
Step: 10
-10y + 2717 = 1477
[Combine like terms.]
Step: 11
-10y = -1240
[Subtract 2717 from each side.]
Step: 12
y = 124
[Divide each side by -10.]
Step: 13
x = -(124) + 209 = 85
[Substitute 124 for y in revised Equation 1.]
Step: 14
85 adults and 124 children went to the circus that day.
Correct Answer is : 85 adults and 124 children