Question

A theater can hold 140 giants or 210 elves. If 90 giants are already inside, how many elves can also be admitted?

Answer 1

I am choosing to make this a ratio problem.

There are 140 giants for every 210 elves (either or in this situation because either 140 giants fit or 210 elves)

Ratios look like this:

140:210 - now we factor both sides - start with 10 since it's easy

14:21 - look for another factor - I see 7

2:3 - this is our ratio of giants to elves

so given 90 giants - what number can be divided by 2/3 to get 90?

(or 90 = 2/3 x)

90 x 3/2 = x which = 270/2 = 135 elves

Check it. 135 x 2/3 = 90. Yes! it checks.

Answer 2

75 elves.

I created a fraction to help solve for the number of elves. I did so by:

90/x=140/210 

I solved for x which would equal 135. This is the equivalent number of elves in the theater. You would subtract this number from 210 which would equal 75.

OR 

You can figure out how many elves equal 1 giant. In this case, you would divide 210 by 140 which equals 1.5 giants. Since there are 90 giants, you multiply 1.5 giants to find out an equivalent for elves which would equal 135. Same as before, subtract this from 210, resulting in 75.