Question

Three fourths of the offspring of two fruit flies have short wings, while the rest have wild-type wings . In a batch of offspring from those two flies, 100 have wild-type wings. How many of the flies have short wings?

Answer 1

300

Explanation:

If three-fourths of the offspring of two fruit flies have short wings and the rest have wild-type wings, then
`1-(3)/(4)=(1)/(4)` of the offspring must have wild-type wings. This means that the number of offspring that have short wings must be
`(3/4)/(1/4)=(3)/(4)\cdot (4)/(1)=3` times larger than the number of offspring that have wild-type wings. Since there are 100 offspring who have wild-type wings, there must be
`100\cdot 3=\boxed{300}` that have short wings.

Alternative:

If three-fourths of the offspring of two fruit flies have short wings and the rest have wild-type wings, then
`1-(3)/(4)=(1)/(4)` of the offspring must have wild-type wings. Therefore, 100 represents one-fourth of the total number of offspring, meaning there must be
`100\cdot 4=400` offspring total. Thus, there are
`400-100=\boxed{300}` offspring with short wings.