Question

A motivational speaker charges $5 for an adult's ticket and $2 for a child's ticket. For one event, he sold 785 tickets for $3280. How many adult tickets were sold? a) 785 b) 570 c) 215 d) 58

Answer 1

the number of adult ticket sold is 570

`x=570`

Step-by-step explanation:

Let x represent the number of adult ticket and y represent the number of child's ticket.

Given that he charges $5 for an adult's ticket and $2 for a child's ticket.

For one event, he sold 785 tickets.

So, we have;

`x+y=785\text{ -----1}`

he sold 785 tickets for $3280.

Then;

`5x+2y=3280\text{ ------2}`

let us solve by substitution.

make y the subject of formula in equation 1 and substitute to equation 2;

`y=785-x`

substituting to equation 2;

`\begin{gathered} 5x+2y=3280 \\ 5x+2(785-x)=3280 \\ 5x+1570-2x=3280 \\ 5x-2x=3280-1570 \\ 3x=1710 \\ x=(1710)/(3) \\ x=570 \end{gathered}`

Therefore, since x represent the number of adult tickets sold, then the number of adult ticket sold is 570

`x=570`