B3. Jana and Jan found that the number of their friends on social media is in the ratio $5: 4$. If Jana had $6 \%$ fewer friends and Jan had $\frac{1}{20}$ more friends, Jana would still have 15 more friends than Jan. How many friends does Jana have?

(7 points)
B3. Let's write Jan: Jan $=5: 4$ or Jana $=5 x$ and Jan $=4 x$. We write the equation with fractions or percentages: $5 x-\frac{6}{100} \cdot 5 x=4 x+\frac{1}{20} \cdot 4 x+15$ or $5 x-6 \% \cdot 5 x=4 x+5 \% \cdot 4 x+15$. We organize the linear equation: $5 x-\frac{3}{10} x=4 x+\frac{x}{5}+15$, multiply by 10 and get $50 x-3 x=40 x+2 x+150$. The solution to the equation is $x=30$. Therefore, Jana has 150 friends and Jan has 120 friends.

![](https://cdn.mathpix.com/cropped/2024_06_07_d6b556bd14f8001ca6fag-11.jpg?height=49&width=1676&top_left_y=1957&top_left_x=230)

![](https://cdn.mathpix.com/cropped/2024_06_07_d6b556bd14f8001ca6fag-11.jpg?height=60&width=1674&top_left_y=2003&top_left_x=228)

![](https://cdn.mathpix.com/cropped/2024_06_07_d6b556bd14f8001ca6fag-11.jpg?height=48&width=1674&top_left_y=2055&top_left_x=228)

![](https://cdn.mathpix.com/cropped/2024_06_07_d6b556bd14f8001ca6fag-11.jpg?height=51&width=1671&top_left_y=2102&top_left_x=231)
Writing the answer: Jana has 150 friends................................................... 1 point