Question

One hundred and fifty tickets were sold for a basketball match and $560 was the total amount collected. Adult tickets were sold at $4 each and child tickets were sold at $1.50 each. How many tickets and how many child tickets were sold?

Answer 1

Answer:

$134$ adult tickets and $16$ child tickets were sold.

Step-by-step explanation:

Let $a$ represents  the number of adult tickets sold and $c$ represents the number of child tickets.

The total number of tickets sold was $150$. So we can write the equation,

$a+c=150...eqn(1)$

Adult tickets were sold at $ $4$ each. This means that, $a$ number of adult tickets will yield $ $4a$.

Child tickets were sold at $ $1.50$ each. This means that, $c$ number of adult tickets will yield $ $1.50c$.

The total amount collected was $ $560$.

We can write this equation for the total amount collected.

$4a+1.50c=560...eqn(2)$

Let us make $a$ the subject in equation (1) to get,

$a=150-c...eqn(3)$

We put equation (3) in to equation (2) to get,

$4(150-c)+1.50c=560$

We expand the brackets to get,

$600-4c+1.50c=560$

We group like terms to get,

$-4c+1.50c=560-600$

$-2.5c=-40$

We divide both sides by $-2.5$ to get,

$c=\frac{-40}{-2.5}$

This implies that,

$c=16$

We substitute $c=16$ into equation (3) to get,

$a=150-16$

$\Rightarrow a=134$

Hence $134$ adult tickets and $16$ child tickets were sold.