Question

If 111 people attend a concert and tickets for adults cost $4 while tickets for children cost $3.25 and total receipts for the concert was $401.25, how many of each went to the concert?

Answer 1

57 children

54 adults

Explanation:

Let's call x the number of children admitted and call z the number of adults admitted.

Then we know that:

`x + z = 111`

We also know that:

`3.25x + 4z = 401.25`

We want to find the value of x and z. Then we solve the system of equations:

-Multiplay the first equation by -4 and add it to the second equation:

`-4x - 4z = -444`

`3.25x + 4z = 401.25`

----------------------------------

`-0.75x = -42.75`

`x =(-42.75)/(-0.75)\\\\x=57`

Now we substitute the value of x in the first equation and solve for the variable z

`57 + z = 111`

`z = 111-57`

`z = 54`

Answer 2

Number of children=57

Number of adults=54

Explanation:

We can start by forming simultaneous equations from the information provided.

Let the number of children be x and adults be y, then the the sum of the amount collected from both children and adults=3.25x+4y=401.25

The total number of people in attendance x+y=111

Let us solve these equations simultaneously.

3.25x+4y=401.25

x+y=111

Using substitution method.

y=111-x

3.25x+4(111-x)=401.25

3.25x+444-4x=401.25

-0.75cx=-42.75

x=57

Number of children=57

Adults=111-57

=54