Answer
There were $210$ adult tickets sold.
Work Step by Step
For this exercise, set up a system of equations: one equation adds up the number of tickets sold while the other equation adds up the amount of money collected from the sale of the tickets.
First, define the variables:
Let $x$ = the number of child tickets sold
Let $y$ = the number of adult tickets sold
Let $4x$ = the amount of money collected from sales of child tickets
Let $6y$ = the amount of money collected from sales of adult tickets
Set up and label the two equations:
1. $x + y = 385$
2. $4x + 6y = 1960$
Multiply equation $1$ by $-4$ so that the $x$ variable can be eliminated when the two equations are added together:
1. $-4(x + y) = -4(385)$
2. $4x + 6y = 1960$
Multiply to simplify:
1. $-4x - 4y = -1540$
2. $4x + 6y = 1960$
Add the two equations:
$2y = 420$
Divide both sides of the equation by $2$:
$y = 210$
There were $210$ adult tickets sold.
