Question

A youth group and their leaders visited mammoth cav. 2 adults and 5 students in one van paid $77 for a tour of the cave. Two adults and 7 students in a second van paid $95 for the same tour. Find the adult price and the student price of the ticket

Answer 1

two more students cost how much more money?

Answer 2

or in simple english, what is \(95-77\)?

Answer 3

but that still makes no sense regarding what the question is asking

Answer 4

why not?

Answer 5

two students cost an extra \(95-77=18\) right?

Answer 6

Okay lets think of our unknowns as variables. Lets just easily calls those variables x & y. What we don't know is how much adults paid and how much a student paid. What we do know is their cost.

I can tell you our goal here is to solve a two linear equations. I'll help you find the first equation from the first part of the question, and i bet you'll be able to get the second one.

\[2x+5y=77\]

Answer 7

if two students cost an extra $18, the price per student is half of that

Answer 8

but it's still asking the price for the student and adult tickets

Answer 9

right
two students cost $18
what is the price of one student?

Answer 10

one student would be $9

Answer 11

yes

Answer 12

and since one student cost $9, then we can figure out what the adult cost since
\[2\times \text{ adult price}+5\times \$9=\$77\]

Answer 13

of if you prefer \[2\times \text{ adult price}+7\times \$9=\$95\] either way

Answer 14

you know how to solve those?

Answer 15

I see, thank you

Answer 16

yw