Question

A group who of 3 adults and 10 students paid $102 for a cavern tour. Another group of 3 adult and 7 students paid $84 for the tour find admission price for an adult ticket and a student.

Answer 1

Admission price for an adult ticket and a student is $14 & $6 respectively .

Step-by-step explanation:

Here we have , A group who of 3 adults and 10 students paid $102 for a cavern tour. Another group of 3 adult and 7 students paid $84 for the tour  .

Linear equation for statement A group who of 3 adults and 10 students paid $102 for a cavern tour:

⇒ $3x + 10y = 102$ , where x is price of adult ticket & y of students .

Linear equation for statement Another group of 3 adult and 7 students paid $84 for the tour :

⇒ $3x+7y= 84$ ,  where x is price of adult ticket & y of students .

subtracting both linear equation we get:

⇒ $(3x+10y)-(3x+7y) = 102-84$

⇒ $3y = 18$

⇒ $y =6$

Putting value of y in equation $3x + 10y = 102$:

⇒  $3x + 10y = 102$

⇒  $3x + 10(6) = 102$

⇒  $3x = 42$

⇒  $x = 14$

∴ Admission price for an adult ticket and a student is $14 & $6 respectively .