Answer:
Number of child tickets = 800
Number of adult tickets = 330
Step-by-step explanation:
Let c = number of child tickets
and a= the number of adult tickets.
We are given:
The admission fee at the steamboat springs hot air balloon festival is $1.50 for children and $4.00 for adults.
On a certain day, 1,130 enter the festival and 2, 520 is collected.
Making equations:
[tex]c+a=1130[/tex] (because total people entered are 1130, so adding number of adult and child tickets will give us total number of people)
[tex]1.50c+4.00a=2520[/tex] (because total money collected is 2520, so adding coat of adult and child tickets will give us total money)
Now, solving these equations simultaneously, we can find values of x and y
Let:
[tex]c+a=1130--eq(1)\\1.50c+4.00a=2520--eq(2)[/tex]
From equation 1 find value of c and put it in eq(2)
[tex]c+a=1130\\c=1130-a[/tex]
Putting value of c in eq(2)
[tex]1.50c+4.00a=2520\\Put\:c=1130-a\\1.5(1130-a)+4a=2520\\1695-1.5a+4a=2520\\-1.5a+4a=2520-1695\\2.5a=825\\a=\frac{825}{2.5}\\a=330[/tex]
So, we get value of a = 330
Now, punting value of a in eq(1) to get value of c
[tex]c+a=1130\\c+330=1130\\c=1130-330\\c=800[/tex]
So, we get value of c = 800
Therefore:
Number of child tickets = c= 800
Number of adult tickets = a = 330
