student tickets for a show cost $5 and adult tickets cost $8. At one show, $2065 was collected in ticket sales. If 62 more students tickets were sold than adult tickets, how many of each type of ticket was sold?

The number of student tickets, we will represent with the variable, s.

The number of adult tickets, we will represent with the variable, a.

Now we convert the next sentence to an mathematical statement, and since student tickets are $5 and adult tickets are $8, we get:

$2065 = $5 * s + $8 * a

Now, the last sentence of the problem:

62 + a = s

Now we have two variables and two equations so we can solve the problem.

Substitute (62 + a) for s in the top equation

$2065 = $5 * (62 + a) + $8 * a

$2065 = $310 + $5 * a + $8 * a

$2065 - $310 = $13 * a

$1755 = $13 * a

a = 135

Now to find s, we use the bottom equation,

s = 62 + a = 62 + 135 = 197