## Task B-1.5.

Ivo and Ana both drank lemonade at the cinema and watched a movie. Ivo took a medium size, and Ana a large one, which is $50\%$ larger than the medium. After both had drunk $\frac{3}{4}$ of their lemonade, Ana gave Ivo one third of what was left to her and an additional 0.5 dl. After the movie ended and they had finished all the lemonade, they found out that they had both drunk the same amount of lemonade. How many deciliters of lemonade did they drink in total?
## Solution.

Let $x$ be the average amount of lemonade Ivo took at the beginning. Ana took $1.5x$.

Ivo received from Ana $\frac{1}{3} \cdot \frac{1}{4} \cdot 1.5 x + 0.5 = \frac{1}{8} x + 0.5$,

which means he drank a total of $x + \frac{1}{8} x + 0.5 = \frac{9}{8} x + 0.5 \text{ dl}$ of lemonade.

Ana drank a total of $1.5 x - \left(\frac{1}{8} x + 0.5\right) = \frac{11}{8} x - 0.5$.

Then, $\frac{11}{8} x - 0.5 = \frac{9}{8} x + 0.5$, 1 point

$\frac{2}{8} x = 1, x = 4$.

The average amount of lemonade is $4 \text{ dl}$, and the total amount they drank is $x + 1.5 x = 2.5 x$, which is $10 \text{ dl}$ of lemonade.