Question

A theater can hold 160 giants or 240 elves. If 109 giants are inside how many elves can also be admitted.

Answer 1

it depends

Explanation:

If the tradeoff between giants and elves is linear, then about 76 elves can be admitted. If it is non-linear, we need more information about the tradeoff.

For example, elves may fit in the spaces between giants in such a way that they take up proportionately less room. Or, elves may repel giants in such a way that they take up proportionately more room.

See the attached graph for some possibilities.

_____

The linear equation can be written as ...

g/160 + e/240 = 1

Then for g=109, we can solve for "e" as ...

109/160 + e/240 = 1

240(1 -109/160) = e = (3/2)(51) = 76.5

If the tradeoff is linear, 76 elves can be admitted.