Math fractions problem? Half of the seats in a theater are full...

Question

Half of the seats in a theater are full. Twenty-four of these people leave so that the theater is now one-third full. How many people would the theater hold if all of the seats were occupied?

Answer 1

Hi Tracey B.,

Let x = the number of seats in the theater.

When the theater is half full, (1/2)x = the half full theater.

When the theater is one third full, (1/3)x = the one third full theater.

When 24 people leave the half full theater, (1/2)x - 24 = one third full theater, (1/3)x.

We have the equation:

(1/2)x - 24 = (1/3)x

Can you solve for x from here?

I have x = 144 seats in the theater.

I hope this helps, Joe.

Answer 2

Half of the seats in a theater are full. Twenty-four of these people leave so that the theater is now one-third full. How many people would the theater hold if all of the seats were occupied?

number of seats in theater = n

Half of the seats in a theater = n/2

1/3 seats in theater = n/3

so when Twenty-four of these people leave

n/2 - 24 = n/3

lcm of denominator is 6

3n - 144 = 2n

3n - 2n = 144

n =144

number of seats in theater = n = 144