Question

On Saturday, some adults and some children were in a theatre.

The ratio of the number of adults to the number of children was 4:3.
Each person had a seat in the Circle or had a seat in the Stalls.
2/3 of the children had seats in the Stalls.
114 children had seats in the Circle.
There are exactly 1100 seats in the theatre.
On this Saturday, were there people on more than 70% of the seats?
You must show how you get your answer

Answer 1

Yes, there were people on more than 70% of the seats.

Explanation:

Let's start with the children. We know that 2/3 of the children had seats in the Stalls, which means that the other 1/3 of the children had seats in the Circle. We know that 114 children had seats in the Circle. Therefore, we can calculate that there were 342 children total, since 114 (1/3 of the children) times 3 is 342.

In order to find how many adults there were, we can use the ratio of adults to children, 4:3. We're basically going to undo our math from the previous part. We divide 342 by 3 to determine how much 1 is. This gives us 114, which we multiply by 4 to find how many adults there were.

There were 456 adults.

There were 342 children.

456 + 342 = 798

There were 798 people in the theatre total.

To find what 70% of 1100 is, we multiply 0.7 x 1100. This gives us 770. Because 798 is more than 770, we know that there were people on more than 70% of the seats.