7) Nineteen students must receive scholarships for a total of 20000 Euros. The amount of each scholarship is expressed as an integer number of Euros. All boys will receive the same amount, and so will the girls. But each girl will receive 600 Euros more than the boys. How much does each boy receive?
(A) 600
(B) 800
(C) 1400
(D) 1600
(E) only the girls receive a scholarship
7) The answer is (B). Let $b$ be the amount of the scholarship and $m$ be the number of boys who receive a scholarship. Then we can write

$$
m \cdot b+(19-m)(b+600)=20000
$$

from which we derive

$$
19 b=200(3 m+43) \text {. }
$$

Since 19 is a prime number, $(3 m+43)$ must be a multiple of $19. \text{But} \frac{3 m+43}{19}=2+\frac{3 m+5}{19}$ and the only $m \leq 19$ that makes this last fraction an integer is $m=11$. Therefore, $b=200 \frac{33+43}{19}=800$.