Question

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 5)3 festival and 2, 520 is collected. Given , = number of child tickets and a= the number of adult tickets. How many children and how many adults attended?

Answer 1

Number of child tickets = 800

Number of adult tickets = 330

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:

`c+a=1130` (because total people entered are 1130, so adding number of adult and child tickets will give us total number of people)

`1.50c+4.00a=2520` (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:

`c+a=1130--eq(1)\\1.50c+4.00a=2520--eq(2)`

From equation 1 find value of c and put it in eq(2)

`c+a=1130\\c=1130-a`

Putting value of c in eq(2)

`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=(825)/(2.5)\\a=330`

So, we get value of a = 330

Now, punting value of a in eq(1) to get value of c

`c+a=1130\\c+330=1130\\c=1130-330\\c=800`

So, we get value of c = 800

Therefore:

Number of child tickets = c= 800

Number of adult tickets = a = 330