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.

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:

⇒ , 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 :

⇒ ,  where x is price of adult ticket & y of students .

subtracting both linear equation we get:

⇒

⇒

⇒

Putting value of y in equation :

⇒  

⇒  

⇒  

⇒  

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

b. 18

step-by-step explanation:

so the equation for this is:

ab^2=ac⋅ad

ab being the top length of 6 and ac being the length of 2 and ad being the length of x. let's plug into the equation:

6^2 = 2x

now lets just solve for x:

36 = 2x

18 = x

i hope that !