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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?

Respuesta :

luisejr77

Answer:

57 children

54 adults

Step-by-step explanation:

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

Then we know that:

[tex]x + z = 111[/tex]

We also know that:

[tex]3.25x + 4z = 401.25[/tex]

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:

[tex]-4x - 4z = -444[/tex]

[tex]3.25x + 4z = 401.25[/tex]

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

[tex]-0.75x = -42.75[/tex]

[tex]x =\frac{-42.75}{-0.75}\\\\x=57[/tex]

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

[tex]57 + z = 111[/tex]

[tex]z = 111-57[/tex]

[tex]z = 54[/tex]

smmwaite

Answer:

Number of children=57

Number of adults=54

Step-by-step 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