Answer:
[tex]134[/tex] adult tickets and [tex]16[/tex] child tickets were sold.
Step-by-step explanation:
Let [tex]a[/tex] represents the number of adult tickets sold and [tex]c[/tex] represents the number of child tickets.
The total number of tickets sold was [tex]150[/tex]. So we can write the equation,
[tex]a+c=150...eqn(1)[/tex]
Adult tickets were sold at $ [tex]4[/tex] each. This means that, [tex]a[/tex] number of adult tickets will yield $ [tex]4a[/tex].
Child tickets were sold at $ [tex]1.50[/tex] each. This means that, [tex]c[/tex] number of adult tickets will yield $ [tex]1.50c[/tex].
The total amount collected was $ [tex]560[/tex].
We can write this equation for the total amount collected.
[tex]4a+1.50c=560...eqn(2)[/tex]
Let us make [tex]a[/tex] the subject in equation (1) to get,
[tex]a=150-c...eqn(3)[/tex]
We put equation (3) in to equation (2) to get,
[tex]4(150-c)+1.50c=560[/tex]
We expand the brackets to get,
[tex]600-4c+1.50c=560[/tex]
We group like terms to get,
[tex]-4c+1.50c=560-600[/tex]
[tex]-2.5c=-40[/tex]
We divide both sides by [tex]-2.5[/tex] to get,
[tex]c=\frac{-40}{-2.5}[/tex]
This implies that,
[tex]c=16[/tex]
We substitute [tex]c=16[/tex] into equation (3) to get,
[tex]a=150-16[/tex]
[tex]\Rightarrow a=134[/tex]
Hence [tex]134[/tex] adult tickets and [tex]16[/tex] child tickets were sold.
