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

Answer:

300

Step-by-step explanation:

If three-fourths of the offspring of two fruit flies have short wings and the rest have wild-type wings, then $1-\frac{3}{4}=\frac{1}{4}$ of the offspring must have wild-type wings. This means that the number of offspring that have short wings must be $\frac{3/4}{1/4}=\frac{3}{4}\cdot \frac{4}{1}=3$ 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 $1-\frac{3}{4}=\frac{1}{4}$ 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.