## Task 3 - 080513

Annerose brings apples and plums from the garden.

When she comes home, her brother Gerd asks: "How many apples and how many plums did you bring?"

With a mischievous smile, Annerose answers: "There are fewer than 50 in total, and there are three times as many plums as apples. If Mother gives each of us four siblings one apple and one plum from the ones I brought, four times as many plums as apples will be left."

How many apples and how many plums did she bring?
Let the number of plums be $p$, and the number of apples be $a$.

From the problem statement, the equations are

$$
p-4=4(a-4) \quad ; \quad p=3 a
$$

Substituting the second equation into the first, we get

$$
3 a-4=4 a-16 \quad \Rightarrow a=12 ; \quad p=36
$$

Annerose brought 12 apples and 36 plums. The condition of the problem, that the sum of $p$ and $a$ must be less than 50, is satisfied.