Answer:
The number of adult that were at fair are 480 adults
The number of children that were at fair are 580 children
Explanation:
The given parameters are;
The entry tickets cost for children = $5
The entry ticket cost for adult = $10
The number of people that entered the fair on a certain day = 1,000
The amount collected for entry tickets sold = $7,100
Let 'x' represent the number of children that bought tickets and were at fair, and let 'y' represent the number of adults that bought tickets and were at the fair, we have;
x + y = 1,000...(1)
5·x + 10·y = 7,100...(2)
Making 'y' the subject of both equations gives;
For equation (1)
y = 1000 - x...(3)
For equation (2)
10·y = 7,100 - 5·x
y = (7,100 - 5·x)/10 = 710 - x/2
y = 710 - x/2...(4)
Equating both values of 'y' from equation (3) and equation (4), we have;
1000 - x = 710 - x/2
1000 - 710 = -x/2 + x = x/2
290 = x/2
x = 580
The number of children that bought tickets and were at fair = x = 580 children
From equation (3), y = 1,000 - x = 1,000 - 580 = 420
y = 480
The number of adult that bought tickets and were at fair = y = 480 adults.