Two workers, $A$ and $B$, completed a certain job; $A$ received 30 pengő, and $B$ received 14 pengő, given that $B$ worked 3 fewer days than $A$.

If $A$ had worked 2 fewer days and $B$ had worked 5 more days, they would have received the same amount. How many days did each work on the job, and what was their daily wage?
Let the number of workdays of $A$ be $x$; thus, the daily wage of $A$ is $\frac{30}{x}$.

The number of workdays of $B$ is $x-3$, and the daily wage of $B$ is $\frac{14}{x-3}$.

If $A$ works for two days less, the earnings are $\frac{30}{x}(x-2)$.

If $B$ works for five more days $(x-3+5=x+2)$, the earnings are $\frac{14}{x-3}(x+2)$.

The requirement of the problem is:

$$
\frac{30}{x}(x-2)=\frac{14}{x-3}(x+2) \quad \text { or equivalently } \quad 30(x-2)(x-3)=14 x(x+2)
$$

After performing the indicated multiplications and simplifying:

$$
8 x^{2}-89 x+90=0 \quad \text { and from this } \quad x_{1}=10, \quad x_{2}=\frac{9}{8}
$$

Since the number of workdays of $B$ is $x-3$, it must be that $x>3$: thus, $x=10$ days.

The daily wage of $A$ is $\frac{30}{10}=3$ pengős, and that of $B$ is $\frac{14}{7}=2$ pengős.

Mária Székely (daughter of Veres Pálné, 4th grade, Bp.)