How do you raise the most money.

Question

There are 180 spots in an auditorium but for every 2 adults there has to be one student. Prices are $14.00 for an adult and $7 for a student how do you get the most money from attendants.

Answer 1

Adults pay the most money, but there needs to be a student for every two This means that our equation information looks like this:

a + s = 180 (the number of adults and students equal 180 seats)

a = 2s (there are twice the number of adults than students)

14a + 7s = m (the ticket costs together give us a certain amount of money)

 

Since we have a value for a, let's put that into our first equation:

2s + s = 180

3s = 180

Divide by 3:

s = 60

 

a = 2 * 60

a = 120

 

Now that we know the number of each age, we can solve for money:

14 * 120 + 7 * 60 = m

1680 + 420 = m

2100 = m

Answer 2

In order to raise the most amount of money we need to have more adults than students so in order to do that we need to consider dividing 180 seats in the ratio 

 

2:1

 

which is 180 / 3 = 60

 

120 adults to 60 child seats would  you the most amount of money which is

 

120(14) + 60(7)

 

= 2100 dollars