Question

A group of three adults and 10 students paid $102 for a cavern tour .Another group of3 adults and 7 students paid $84 for the tour.Find the admission price for an adult ticket and a student ticket.

Answer 1

Let admission price of adults be x

and

Let admission price of students be y

Equation for the first group=> 3x+10y= 102

Equation for the second group=> 3x+7y= 84

Now, let's subtract these equations

$\: \: \: 3x + 10y = 102 \\ - (3x + 7y) = 84$

$3x + 10y = 102 \\ - 3x - 7y = - 84$

$3y = 18$

$y = 6$

Putting this value in eq

$3x + 10 \times 6 = 102$

$3x + 60 = 102$

$3x = 102 - 60$

$3x = 42 \\ x = \frac{42}{3} \\ x = 14$

So, the admission price of adult is $14

The admission price of student is $6