word problem

Question

A youth group and their leaders visited Mammoth Cave, two adults and 5 students in one van paid $77 for the Grand Avenue 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 tour.

Answer 1

Let's set up a system of equations. We're trying to find the adult price and the student price, so let a= adult price and s= student price.

 

Equation 1: 2a + 5s = $77

Equation 2: 2a + 7s = $95

 

Notice that there are two adults in each equation. That means the difference in the price each group paid is because of the difference in the number of students! So you can actually just find the difference between the two equations and solve for s, and you will be headed in the right direction!

 

Equation 2 - Equation 1: 0a + 2s = $18

s = $9

 

Now substitute s into either equation, and you'll find the adult price:

2a + 5(9) = 77

2a + 45 = 77

2a = 32

a = $16